Load Packages

library(ggplot2)
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.2     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ lubridate 1.9.2     ✔ tibble    3.2.1
## ✔ purrr     1.0.2     ✔ tidyr     1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(dplyr)
library(meta)
## Loading 'meta' package (version 6.5-0).
## Type 'help(meta)' for a brief overview.
## Readers of 'Meta-Analysis with R (Use R!)' should install
## older version of 'meta' package: https://tinyurl.com/dt4y5drs
library(PRISMAstatement)
library(skimr)
library(MASS)
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
library(ggpubr)
setwd("~/Desktop/Chapter 4")
photo <- read.csv("observations_2022.csv")
summary(photo)
##     region              site            site_code          microsite        
##  Length:58015       Length:58015       Length:58015       Length:58015      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##       plot           cam_ID         month                day       
##  Min.   :1.000   Min.   :1.000   Length:58015       Min.   : 3.00  
##  1st Qu.:1.000   1st Qu.:1.000   Class :character   1st Qu.: 6.00  
##  Median :1.000   Median :2.000   Mode  :character   Median :16.00  
##  Mean   :1.775   Mean   :1.527                      Mean   :13.98  
##  3rd Qu.:2.000   3rd Qu.:2.000                      3rd Qu.:22.00  
##  Max.   :4.000   Max.   :2.000                      Max.   :29.00  
##       year      shrub_density         rep        identified_by     
##  Min.   :2022   Min.   : 0.000   Min.   :    1   Length:58015      
##  1st Qu.:2022   1st Qu.: 0.000   1st Qu.: 5386   Class :character  
##  Median :2022   Median : 0.000   Median :12638   Mode  :character  
##  Mean   :2022   Mean   : 4.681   Mean   :15170                     
##  3rd Qu.:2022   3rd Qu.:11.000   3rd Qu.:24318                     
##  Max.   :2022   Max.   :14.000   Max.   :38822                     
##    filename          timestamp           animal.hit         class          
##  Length:58015       Length:58015       Min.   :0.00000   Length:58015      
##  Class :character   Class :character   1st Qu.:0.00000   Class :character  
##  Mode  :character   Mode  :character   Median :0.00000   Mode  :character  
##                                        Mean   :0.06521                     
##                                        3rd Qu.:0.00000                     
##                                        Max.   :1.00000                     
##     order              family             genus             species         
##  Length:58015       Length:58015       Length:58015       Length:58015      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  common_name        number_of_objects
##  Length:58015       Min.   : 1.000   
##  Class :character   1st Qu.: 1.000   
##  Mode  :character   Median : 1.000   
##                     Mean   : 1.001   
##                     3rd Qu.: 1.000   
##                     Max.   :12.000
photo <- photo %>%
  filter(common_name != "Human")
photo <- photo %>%
  filter(common_name != "Human-Camera Trapper")
photo <- photo %>%
  filter(common_name != "Domestic Dog")
photo <- photo %>%
  filter(common_name != "Vehicle")
photo <- photo %>%
  dplyr::filter(common_name != "Insect")
photo <- photo %>%
  dplyr::filter(common_name != "Animal")
photo <- photo %>%
  dplyr::filter(common_name != "Bird")
photo <- photo %>%
  filter(common_name != "No CV Result")
  
count.hit <- photo %>%
  count(animal.hit) %>%
  na.omit()
summary(count.hit)
##    animal.hit         n        
##  Min.   :0.00   Min.   : 3169  
##  1st Qu.:0.25   1st Qu.:15935  
##  Median :0.50   Median :28700  
##  Mean   :0.50   Mean   :28700  
##  3rd Qu.:0.75   3rd Qu.:41466  
##  Max.   :1.00   Max.   :54232
### 2022 Had a 5.88% catch rate
### Animal Observations by Site_Code
animals_by_sitecode <- photo%>%
  group_by(site_code, microsite, common_name) %>%
  summarise(captures = sum(animal.hit), n = n())
## `summarise()` has grouped output by 'site_code', 'microsite'. You can override
## using the `.groups` argument.
animals_by_sitecode <- animals_by_sitecode %>%
  filter(common_name != "Blank") 
### Animal observations by Site
animals_by_site <- photo %>% group_by(site,microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site', 'microsite'. You can override using
## the `.groups` argument.
animals_by_site <- animals_by_site %>% filter(common_name != "Blank")
### Animal observations by Density
animals_by_density <- photo %>% group_by(microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'microsite'. You can override using the
## `.groups` argument.
animals_by_density <- animals_by_density %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result")
### Total Observations 2022
Total_Observations <- photo %>% group_by(common_name) %>% summarise(total = sum(animal.hit)) %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result")
density_obvs <- merge(animals_by_density, Total_Observations, all = TRUE)
density_obvs$percent_presence <- density_obvs$captures/density_obvs$total
### Percent proportion Figure
plot1 <- ggplot(density_obvs, aes(common_name, percent_presence, fill = microsite)) + geom_bar(stat = "identity") + coord_flip() + theme_classic() + scale_x_discrete(limits=rev) + xlab("Species") + ylab("Percent Proportion") + labs(fill = "Microsite")
plot1 + scale_fill_manual(values = c("#009900", "#0066cc"))

library(emmeans)
m1 <- glm(total ~ microsite*common_name, family = "poisson", data = density_obvs)
anova(m1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: total
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                                     44      22806             
## microsite              1      5.4        43      22801  0.01984 *  
## common_name           26  22800.9        17          0  < 2e-16 ***
## microsite:common_name 17      0.0         0          0  1.00000    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e1 <- emmeans(m1, pairwise~common_name)
## NOTE: Results may be misleading due to involvement in interactions
#head(e1)
animals_density <- photo %>% group_by(site_code,microsite,plot, shrub_density, common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site_code', 'microsite', 'plot',
## 'shrub_density'. You can override using the `.groups` argument.
animals_density <- animals_density %>% filter(common_name != "Blank") %>% filter(common_name != "No CV Result")

All current PCOA code for 2022 only

### PCA
library(vegan)
## Loading required package: permute
## Loading required package: lattice
## This is vegan 2.6-4
library(ape) ### For PCOA
## 
## Attaching package: 'ape'
## The following object is masked from 'package:ggpubr':
## 
##     rotate
## The following object is masked from 'package:dplyr':
## 
##     where
pca_data <- animals_density ### Created new df for pca data
pca_data <- pca_data %>%
  spread(common_name, captures) %>%
  ungroup() %>%
  dplyr::select(-site_code, -microsite, -plot) %>%
  replace(is.na(.),0)
dim(pca_data)
## [1] 22 28
env <- read.csv("environment.csv") ### Drop Tecopa open 1, Tecopa open 4, since they have no animal observations.
dim(env)
## [1] 22  5
m01 <- adonis(pca_data ~ microsite*shrub_density, data = env)
## 'adonis' will be deprecated: use 'adonis2' instead
m01
## $aov.tab
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##               Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
## microsite      1    0.2242 0.22425 0.76358 0.03600  0.592
## shrub_density  1    0.4245 0.42452 1.44550 0.06815  0.199
## Residuals     19    5.5799 0.29368         0.89584       
## Total         21    6.2287                 1.00000       
## 
## $call
## adonis(formula = pca_data ~ microsite * shrub_density, data = env)
## 
## $coefficients
##                          shrub_density American Robin Black-tailed Jackrabbit
## (Intercept)                  -4.757692   5.000000e-02              -13.455128
## microsite1                   -6.857692  -5.000000e-02              -18.955128
## shrub_density                 1.876923   1.823528e-17                4.184615
## microsite1:shrub_density            NA             NA                      NA
##                          Blunt-nosed Leopard Lizard     Bobcat
## (Intercept)                               0.9987179 -0.6602564
## microsite1                                0.8987179 -1.1602564
## shrub_density                            -0.1538462  0.1692308
## microsite1:shrub_density                         NA         NA
##                          Brewer's Blackbird California Ground Squirrel
## (Intercept)                      0.18717949                  20.411538
## microsite1                      -0.21282051                  13.511538
## shrub_density                    0.06153846                  -1.815385
## microsite1:shrub_density                 NA                         NA
##                          California Pocket Mouse California Quail
## (Intercept)                           0.35641026       -4.2487179
## microsite1                            0.15641026       -5.6487179
## shrub_density                        -0.03076923        0.9538462
## microsite1:shrub_density                      NA               NA
##                          California Thrasher Common Raven     Coyote
## (Intercept)                       -1.4743590    0.7910256  1.4923077
## microsite1                        -1.4743590   -3.5089744 -4.1076923
## shrub_density                      0.2769231    0.3230769  0.4769231
## microsite1:shrub_density                  NA           NA         NA
##                          Desert Cottontail Desert Iguana Giant Kangaroo Rat
## (Intercept)                     -24.729487    2.07820513          6.9935897
## microsite1                      -26.629487   -1.82179487          4.4935897
## shrub_density                     4.861538   -0.01538462         -0.7692308
## microsite1:shrub_density                NA            NA                 NA
##                          Great White Egret Greater Roadrunner
## (Intercept)                   5.000000e-02         -4.3730769
## microsite1                   -5.000000e-02         -4.4730769
## shrub_density                 1.076807e-17          0.8307692
## microsite1:shrub_density                NA                 NA
##                          Heermann's Kangaroo Rat      Killdeer     Kit Fox
## (Intercept)                           140.330769  5.000000e-02  0.44487179
## microsite1                             59.130769 -5.000000e-02  0.14487179
## shrub_density                          -7.707692  6.937479e-18 -0.01538462
## microsite1:shrub_density                      NA            NA          NA
##                          Lark Sparrow Loggerhead Shrike Mohave Ground Squirrel
## (Intercept)                -1.8384615        -0.5935897             0.81923077
## microsite1                 -2.2384615        -0.8935897             0.71923077
## shrub_density               0.3846154         0.1692308            -0.09230769
## microsite1:shrub_density           NA                NA                     NA
##                          Mourning Dove Nelson's Antelope Squirrel
## (Intercept)                 -1.9384615                  18.984615
## microsite1                  -2.1384615                  13.784615
## shrub_density                0.3846154                  -2.246154
## microsite1:shrub_density            NA                         NA
##                          Red-tailed Hawk Salinas Pocket Mouse Vesper Sparrow
## (Intercept)                   -0.5641026         5.000000e-02   5.000000e-02
## microsite1                    -0.5641026        -5.000000e-02  -5.000000e-02
## shrub_density                  0.1076923         1.076807e-17   6.937479e-18
## microsite1:shrub_density              NA                   NA             NA
## 
## $coef.sites
##                                    1           2           3           4
## (Intercept)               0.72187241  0.84634032  1.11978420  0.78585052
## microsite1                0.19194029  0.33115230  0.42744428  0.26477687
## shrub_density            -0.03063205 -0.05640075 -0.06512504 -0.03711672
## microsite1:shrub_density          NA          NA          NA          NA
##                                   5           6           7           8
## (Intercept)               0.7805666  0.70692759  0.95262164  0.80543797
## microsite1                0.2293742  0.15739580  0.22071669  0.25186788
## shrub_density            -0.0393115 -0.02414532 -0.02857079 -0.03727318
## microsite1:shrub_density         NA          NA          NA          NA
##                                   9         10          11          12
## (Intercept)               1.7428122  1.4970441  0.99852391  1.06366871
## microsite1                1.0220992  0.8596173  0.44864549  0.53735308
## shrub_density            -0.1847971 -0.1548735 -0.07052619 -0.08656954
## microsite1:shrub_density         NA         NA          NA          NA
##                                   13           14          15          16
## (Intercept)               0.82385406  0.795551518  0.79238103  0.84065136
## microsite1                0.12690322  0.021850057  0.21124835  0.30308675
## shrub_density            -0.02568071 -0.008853955 -0.02915258 -0.04325977
## microsite1:shrub_density          NA           NA          NA          NA
##                                   17          18          19          20
## (Intercept)               0.38555800  0.50980072  0.68786923  0.55515661
## microsite1               -0.59216512 -0.43255379 -0.20343288 -0.30788751
## shrub_density             0.09323238  0.06736799  0.02712249  0.04455634
## microsite1:shrub_density          NA          NA          NA          NA
##                                    21          22
## (Intercept)               0.881696341  0.64736295
## microsite1                0.013954406 -0.20302121
## shrub_density            -0.001421805  0.02954886
## microsite1:shrub_density           NA          NA
## 
## $f.perms
##               [,1]        [,2]
##    [1,] 0.51232234 2.473580584
##    [2,] 0.49704227 1.354522877
##    [3,] 0.52697747 2.999162560
##    [4,] 0.50159378 1.112610936
##    [5,] 0.35748234 0.433008035
##    [6,] 0.81978454 1.143168562
##    [7,] 0.59669034 0.268670214
##    [8,] 1.00688936 1.029652890
##    [9,] 1.15780782 0.858601644
##   [10,] 3.89781386 0.644123834
##   [11,] 0.52030537 1.698905230
##   [12,] 1.62795975 0.978406120
##   [13,] 1.00678867 0.844647685
##   [14,] 0.53481867 0.176443763
##   [15,] 1.44174975 0.594217705
##   [16,] 0.61611860 0.989803128
##   [17,] 0.91864835 0.286766250
##   [18,] 2.64497631 0.673405539
##   [19,] 0.42536604 0.681951346
##   [20,] 1.73878143 0.374036871
##   [21,] 1.10221417 2.093689181
##   [22,] 0.63496049 0.509472870
##   [23,] 1.09809428 1.196762517
##   [24,] 2.21326320 0.832747600
##   [25,] 0.51845280 0.329327758
##   [26,] 0.68178433 0.978852789
##   [27,] 1.00707132 0.852385361
##   [28,] 2.65152874 1.577666803
##   [29,] 0.71714657 0.377430552
##   [30,] 1.29562492 1.000394381
##   [31,] 0.44634205 1.535223223
##   [32,] 0.65175149 0.950133556
##   [33,] 0.83122592 0.712003997
##   [34,] 0.83901689 0.709685482
##   [35,] 0.35144226 1.261103502
##   [36,] 0.97423126 0.486399131
##   [37,] 1.41654411 1.139195360
##   [38,] 2.63183509 0.822422225
##   [39,] 0.63045381 1.048812011
##   [40,] 0.57146521 0.235203844
##   [41,] 0.58255103 1.075553654
##   [42,] 0.83195385 3.509805522
##   [43,] 0.43876560 0.674938357
##   [44,] 3.03205793 1.528627198
##   [45,] 0.73541826 0.548975511
##   [46,] 0.81734820 1.135478497
##   [47,] 0.66520515 0.939356479
##   [48,] 2.22233465 0.835377447
##   [49,] 1.03708524 1.225118334
##   [50,] 0.24051637 0.002562186
##   [51,] 0.44912974 1.786818579
##   [52,] 1.09840206 0.777684139
##   [53,] 0.12242519 1.136480694
##   [54,] 0.94624480 0.281972197
##   [55,] 0.85764049 1.098086792
##   [56,] 0.92945815 0.727322182
##   [57,] 1.12233361 1.710313997
##   [58,] 0.34049949 2.396354200
##   [59,] 0.21264498 1.014498396
##   [60,] 0.42134724 0.901190137
##   [61,] 1.07287911 0.754105954
##   [62,] 1.55224313 2.083504836
##   [63,] 0.54034848 0.520172598
##   [64,] 0.58094094 1.124299095
##   [65,] 0.44621573 1.405196331
##   [66,] 0.75839148 1.455369432
##   [67,] 0.69548753 1.645188107
##   [68,] 0.67580723 1.139070681
##   [69,] 1.02986205 0.563966151
##   [70,] 0.73676292 0.680581554
##   [71,] 0.30295915 0.208467470
##   [72,] 0.75661983 0.517700811
##   [73,] 1.22171119 1.806591956
##   [74,] 1.22569404 1.518518351
##   [75,] 1.14363340 0.983341434
##   [76,] 0.55592047 1.575122426
##   [77,] 1.06294668 0.558330705
##   [78,] 1.37037649 0.320916716
##   [79,] 1.89467743 0.872142426
##   [80,] 0.67500443 1.761222143
##   [81,] 1.28675605 2.417388870
##   [82,] 1.54805396 0.698164543
##   [83,] 1.45547508 2.028182509
##   [84,] 0.58763708 0.599658980
##   [85,] 0.92807687 1.709026930
##   [86,] 0.64005088 0.740102236
##   [87,] 0.54578394 0.801595372
##   [88,] 1.79599479 1.500531928
##   [89,] 0.90133443 0.703227840
##   [90,] 0.69936616 2.191048073
##   [91,] 0.93875726 0.596185445
##   [92,] 0.75607402 0.525345798
##   [93,] 0.34584872 0.741909916
##   [94,] 0.76470944 1.565698144
##   [95,] 0.63404972 0.454078514
##   [96,] 0.50472178 0.310272503
##   [97,] 1.16018927 1.366538857
##   [98,] 0.08559623 0.654547986
##   [99,] 0.62574935 1.697578182
##  [100,] 1.53250519 0.530083411
##  [101,] 0.77964609 1.022860016
##  [102,] 0.16220950 1.118423459
##  [103,] 0.22724450 1.183286670
##  [104,] 0.97820090 2.323884974
##  [105,] 1.27440256 0.898004413
##  [106,] 0.52178300 2.160333342
##  [107,] 0.60915301 0.634713157
##  [108,] 0.97531782 0.774424849
##  [109,] 1.02979915 1.996457404
##  [110,] 1.21128766 0.661318725
##  [111,] 1.13742991 0.794475584
##  [112,] 1.49480314 1.257785092
##  [113,] 0.30630329 1.819060124
##  [114,] 1.04313623 0.190612673
##  [115,] 1.12720208 0.743063741
##  [116,] 1.71456332 0.764395268
##  [117,] 0.82433685 0.423892531
##  [118,] 0.58157710 1.630981442
##  [119,] 0.50645232 0.588688186
##  [120,] 0.87989761 2.113158815
##  [121,] 0.74103795 1.121913244
##  [122,] 0.20549892 0.790080489
##  [123,] 2.71337090 0.404841827
##  [124,] 2.08278409 0.653325661
##  [125,] 0.93174442 0.681066462
##  [126,] 0.53060081 0.640613406
##  [127,] 0.64917668 0.479552931
##  [128,] 0.49404401 1.190187002
##  [129,] 0.21844911 0.413878150
##  [130,] 0.81111435 0.580928697
##  [131,] 2.47704413 0.527467157
##  [132,] 1.24331927 1.071854038
##  [133,] 0.42672390 0.456200346
##  [134,] 0.41211975 0.337075645
##  [135,] 0.77147751 1.754845752
##  [136,] 2.80238185 0.980626951
##  [137,] 0.70120935 0.489127611
##  [138,] 0.51760489 0.397512047
##  [139,] 1.33572607 0.775856272
##  [140,] 0.86623847 0.792813953
##  [141,] 0.21844221 1.167942045
##  [142,] 0.54186621 1.790142643
##  [143,] 0.61618076 0.262524246
##  [144,] 0.47844914 0.631887512
##  [145,] 1.50828340 0.959079815
##  [146,] 1.98948838 0.598728907
##  [147,] 0.73863087 1.181904896
##  [148,] 0.96532303 0.590855456
##  [149,] 0.67078956 0.542555851
##  [150,] 0.51252224 0.585690971
##  [151,] 1.53080097 0.618156610
##  [152,] 1.02904577 0.978899670
##  [153,] 0.67012349 0.991294697
##  [154,] 0.90908833 0.451544514
##  [155,] 0.28180438 1.288455029
##  [156,] 2.61339834 0.597262362
##  [157,] 0.27143583 1.082892473
##  [158,] 0.89221906 0.229567738
##  [159,] 0.62089282 1.734210019
##  [160,] 0.84474508 0.761334031
##  [161,] 2.91762355 0.325307744
##  [162,] 1.03787067 2.799887781
##  [163,] 2.40749044 0.734041427
##  [164,] 1.00450343 1.353985666
##  [165,] 1.58608192 1.623462864
##  [166,] 0.38291788 2.485125543
##  [167,] 1.85305223 1.308823956
##  [168,] 0.58005503 1.262691666
##  [169,] 0.20021482 1.984416492
##  [170,] 0.97660894 0.781709905
##  [171,] 3.37901418 1.112114707
##  [172,] 1.68910183 0.650252489
##  [173,] 0.77721191 0.884328887
##  [174,] 1.02872283 0.698492493
##  [175,] 0.98789064 0.296907917
##  [176,] 0.48418149 1.114408489
##  [177,] 0.45361011 0.655883174
##  [178,] 1.75633045 1.132250677
##  [179,] 1.10427015 1.118347770
##  [180,] 1.01999422 1.859835107
##  [181,] 0.75777989 0.894708631
##  [182,] 0.97042288 1.103463852
##  [183,] 1.75662757 0.349112567
##  [184,] 0.67588475 0.168502740
##  [185,] 0.97684174 0.812856488
##  [186,] 1.45523223 1.538975860
##  [187,] 0.54463059 0.891326940
##  [188,] 0.58353773 0.624505095
##  [189,] 0.38845770 1.076507368
##  [190,] 0.57444286 1.665662335
##  [191,] 0.56686182 0.812278388
##  [192,] 0.85659490 0.756985254
##  [193,] 1.47935058 0.329484511
##  [194,] 1.27263244 0.909294992
##  [195,] 1.08360812 0.793447319
##  [196,] 1.64618286 3.237726891
##  [197,] 1.78992987 2.395211356
##  [198,] 1.06063522 0.376182460
##  [199,] 1.30894628 0.579133893
##  [200,] 0.20860238 0.621766928
##  [201,] 1.16333347 1.638154744
##  [202,] 0.73435879 2.921689122
##  [203,] 0.57943298 0.715926849
##  [204,] 0.93432456 1.144944795
##  [205,] 0.76370199 2.454283420
##  [206,] 2.14441054 3.420120121
##  [207,] 2.06441082 0.408806969
##  [208,] 0.68568017 0.232972854
##  [209,] 0.81965078 0.574955501
##  [210,] 0.12406883 0.825261763
##  [211,] 0.90989870 1.081156849
##  [212,] 0.62497716 1.359472503
##  [213,] 1.02440396 1.550035353
##  [214,] 1.36581875 1.543304184
##  [215,] 0.82390193 1.590579705
##  [216,] 1.27617714 0.909530951
##  [217,] 2.04132883 0.503879570
##  [218,] 0.83479711 0.561385838
##  [219,] 0.84353445 0.803449469
##  [220,] 0.37827236 1.206018242
##  [221,] 0.91058391 0.648031672
##  [222,] 2.39105907 0.267986595
##  [223,] 0.66460293 1.422136729
##  [224,] 0.45037880 0.218573672
##  [225,] 0.74383682 0.592309102
##  [226,] 0.41792194 0.686902835
##  [227,] 1.57561406 1.371188433
##  [228,] 1.49563458 0.931036909
##  [229,] 0.88386721 1.540874986
##  [230,] 0.97980989 2.311973030
##  [231,] 1.57712188 0.811628898
##  [232,] 0.90728381 1.097855429
##  [233,] 0.63621813 1.406945175
##  [234,] 1.10551226 0.508971828
##  [235,] 0.75996718 0.296048592
##  [236,] 0.08641621 1.031998597
##  [237,] 0.92073684 0.289927649
##  [238,] 0.64939535 0.331068507
##  [239,] 0.72423280 0.765129260
##  [240,] 0.46233167 2.110523171
##  [241,] 0.52164172 1.012960949
##  [242,] 0.45146424 0.593347050
##  [243,] 1.23037674 0.863137931
##  [244,] 0.27430669 1.147904558
##  [245,] 0.64580246 1.391853817
##  [246,] 0.47136092 0.872758247
##  [247,] 1.11795060 2.390291166
##  [248,] 0.37648207 0.676960514
##  [249,] 2.40768832 0.647318270
##  [250,] 0.40913310 2.339644264
##  [251,] 0.58724466 0.798466540
##  [252,] 0.26357686 0.910644427
##  [253,] 1.60888070 1.268255343
##  [254,] 0.88539653 0.209254068
##  [255,] 0.51108855 0.712873842
##  [256,] 0.89966060 1.801873567
##  [257,] 0.74825863 0.570322467
##  [258,] 0.49363372 1.608451857
##  [259,] 0.95383910 0.672886973
##  [260,] 0.85155828 0.705897215
##  [261,] 0.36667542 0.474733464
##  [262,] 2.86383601 0.893825961
##  [263,] 1.19860245 1.109237501
##  [264,] 1.27055895 1.530186229
##  [265,] 0.16508374 1.224681450
##  [266,] 0.87305044 1.447158432
##  [267,] 1.07225831 0.982119774
##  [268,] 1.02534443 1.132125538
##  [269,] 0.96562052 1.494729314
##  [270,] 1.02523755 0.685279947
##  [271,] 0.87141653 1.440798814
##  [272,] 0.42041937 1.431745793
##  [273,] 5.06796145 0.724222884
##  [274,] 0.95421210 1.139950727
##  [275,] 1.11506936 1.663116514
##  [276,] 0.30502480 1.387133260
##  [277,] 0.79884209 0.930818939
##  [278,] 1.50484779 1.216406917
##  [279,] 1.49835667 2.682489798
##  [280,] 1.22546929 0.427694743
##  [281,] 1.18368725 0.670846148
##  [282,] 0.47674729 1.719802913
##  [283,] 0.53636783 1.428197834
##  [284,] 0.77746518 0.677558942
##  [285,] 0.53684673 1.211660139
##  [286,] 0.41923907 0.434950404
##  [287,] 0.27852296 0.648955584
##  [288,] 0.73305007 0.944797784
##  [289,] 0.97398047 0.392622522
##  [290,] 0.87841092 0.422695724
##  [291,] 1.21427766 1.081844128
##  [292,] 1.14551025 1.342353403
##  [293,] 0.59601657 0.913640687
##  [294,] 2.15892619 1.461194491
##  [295,] 0.76848891 0.587953005
##  [296,] 3.21357079 1.258571698
##  [297,] 1.80474011 0.982627122
##  [298,] 0.71827926 1.579378056
##  [299,] 2.24383361 0.742558871
##  [300,] 1.12585012 1.408010766
##  [301,] 0.11180723 0.510948850
##  [302,] 1.39240374 2.094450214
##  [303,] 0.74649620 0.429135306
##  [304,] 0.52461134 1.208722026
##  [305,] 0.45157187 0.410320076
##  [306,] 0.83061779 0.651296701
##  [307,] 2.22519389 0.467273747
##  [308,] 0.58398092 0.457543133
##  [309,] 0.70731957 2.139139101
##  [310,] 0.73669448 0.866219579
##  [311,] 0.37622056 1.026346298
##  [312,] 1.08962229 1.046537829
##  [313,] 1.35592259 0.378100423
##  [314,] 1.76671524 0.529677206
##  [315,] 0.88075142 1.738917832
##  [316,] 0.38953418 0.880133430
##  [317,] 0.37020515 0.902632946
##  [318,] 1.31602860 0.833731632
##  [319,] 1.36412018 0.425147455
##  [320,] 0.69827889 0.588466389
##  [321,] 2.37769604 0.390709091
##  [322,] 1.20549356 0.920469118
##  [323,] 1.75372986 1.784008756
##  [324,] 1.70124632 1.886714473
##  [325,] 0.74250068 0.927857264
##  [326,] 0.61029934 0.621365190
##  [327,] 0.95559791 0.844819192
##  [328,] 0.57638913 1.215040740
##  [329,] 0.60724491 0.931048022
##  [330,] 0.63842637 0.418655832
##  [331,] 0.97474315 1.404174927
##  [332,] 1.61093363 2.812183994
##  [333,] 0.77569172 0.677993683
##  [334,] 2.11108827 0.688749114
##  [335,] 1.02319168 0.747922026
##  [336,] 0.30169467 0.719477645
##  [337,] 0.25398826 0.753110665
##  [338,] 0.96421679 1.393342990
##  [339,] 2.23025819 0.236276143
##  [340,] 0.46820131 0.774277106
##  [341,] 2.11464597 0.201601150
##  [342,] 1.63199916 0.471526744
##  [343,] 0.66281707 0.786055404
##  [344,] 0.20651663 1.226122123
##  [345,] 0.88957444 0.997614309
##  [346,] 1.02681344 1.610476768
##  [347,] 0.91367784 1.476582929
##  [348,] 1.04775292 1.250547664
##  [349,] 3.41627246 1.624884414
##  [350,] 0.46150865 1.525842914
##  [351,] 1.01743411 3.065546557
##  [352,] 0.96216660 0.514327634
##  [353,] 0.49047019 0.668636289
##  [354,] 1.56260356 0.226992606
##  [355,] 1.35561277 3.042103619
##  [356,] 1.15490518 1.518902371
##  [357,] 1.17408305 1.771845623
##  [358,] 0.84563492 0.599269364
##  [359,] 1.67670187 2.609930940
##  [360,] 0.26972333 0.899161865
##  [361,] 1.05086988 1.764899887
##  [362,] 1.04564904 1.249996590
##  [363,] 0.63076710 0.974260533
##  [364,] 2.69138755 0.836520424
##  [365,] 0.82319608 0.195604826
##  [366,] 0.40002082 0.713865561
##  [367,] 2.36946707 1.375780342
##  [368,] 0.74710145 0.991851607
##  [369,] 0.76179807 1.270771083
##  [370,] 2.38591277 0.861387322
##  [371,] 0.95729164 1.013834950
##  [372,] 2.18303325 0.417348241
##  [373,] 1.85528803 2.149361144
##  [374,] 0.48840350 0.401131193
##  [375,] 0.90343999 0.804507479
##  [376,] 0.67633993 0.998176411
##  [377,] 1.52368203 0.743544202
##  [378,] 1.04378738 1.553714765
##  [379,] 2.63921687 1.180010580
##  [380,] 1.10221864 1.500073875
##  [381,] 0.80374630 0.477520458
##  [382,] 0.86453032 1.886758740
##  [383,] 0.17197640 0.758810976
##  [384,] 1.76129788 1.707335272
##  [385,] 1.01205489 1.202799783
##  [386,] 0.43476628 1.137900063
##  [387,] 0.45684503 1.066461144
##  [388,] 1.37673927 1.188340965
##  [389,] 0.90410560 1.252753663
##  [390,] 1.78615829 1.636082722
##  [391,] 1.06111054 1.430288293
##  [392,] 1.52086777 1.009355183
##  [393,] 0.49303026 0.403678132
##  [394,] 0.40492154 1.116212322
##  [395,] 0.64402535 0.686799541
##  [396,] 0.91173020 1.150341237
##  [397,] 1.32612023 1.477900448
##  [398,] 1.16297299 0.642463110
##  [399,] 1.98747459 0.454416869
##  [400,] 0.86591355 0.675373305
##  [401,] 0.35410277 0.586342609
##  [402,] 1.15065091 0.639116807
##  [403,] 0.88080660 0.261934288
##  [404,] 0.99947535 0.979193970
##  [405,] 1.88989565 1.181950697
##  [406,] 0.86312063 1.209696805
##  [407,] 3.52607783 3.468021769
##  [408,] 0.17309078 0.747382308
##  [409,] 0.87918059 0.955497316
##  [410,] 0.78382155 0.379112042
##  [411,] 1.08266138 0.291353866
##  [412,] 3.04103642 1.059222432
##  [413,] 0.95750916 1.671551289
##  [414,] 0.63737456 0.686176706
##  [415,] 0.88998897 0.505488441
##  [416,] 0.63650675 0.802746555
##  [417,] 0.24352658 0.625479645
##  [418,] 0.92901647 1.009366763
##  [419,] 1.09559085 0.479445858
##  [420,] 0.81272264 0.755161208
##  [421,] 0.76851800 0.420275113
##  [422,] 1.26536276 0.445248086
##  [423,] 1.24956400 0.546567476
##  [424,] 0.89301603 1.237613284
##  [425,] 0.99866332 1.006115767
##  [426,] 0.55505850 2.333337878
##  [427,] 1.10643451 0.175214786
##  [428,] 0.48957481 0.789943424
##  [429,] 0.80665655 0.640626094
##  [430,] 2.49064174 5.470125623
##  [431,] 0.58971237 0.874838999
##  [432,] 0.85884268 1.646104541
##  [433,] 0.40977443 1.415080620
##  [434,] 1.65460462 0.910521483
##  [435,] 0.36092007 1.121432549
##  [436,] 0.60433644 3.461802145
##  [437,] 0.80999292 1.231367900
##  [438,] 0.48747918 0.932391063
##  [439,] 0.64899857 0.809687038
##  [440,] 0.82581936 0.344874803
##  [441,] 1.61241207 1.059985453
##  [442,] 1.96632606 0.960397155
##  [443,] 0.75429402 0.575123226
##  [444,] 1.11883983 0.523210163
##  [445,] 1.05547341 0.501884657
##  [446,] 1.25115069 1.419574887
##  [447,] 1.13670637 0.217363190
##  [448,] 0.54564916 1.238969183
##  [449,] 2.25155265 1.655703463
##  [450,] 1.10228077 1.195962726
##  [451,] 1.20952502 0.714655846
##  [452,] 0.79691884 3.940732569
##  [453,] 1.62884928 1.301872933
##  [454,] 0.25681016 0.334368451
##  [455,] 1.63445087 1.017426645
##  [456,] 0.98675598 0.079352716
##  [457,] 0.31242518 0.917235931
##  [458,] 0.70099623 1.183828719
##  [459,] 1.53060047 0.536672498
##  [460,] 0.59562380 0.797615693
##  [461,] 0.81636447 0.596810386
##  [462,] 1.76322670 0.683910302
##  [463,] 0.59559382 0.662930832
##  [464,] 0.66289910 1.384121690
##  [465,] 1.51276813 0.804108840
##  [466,] 0.31593172 0.801978016
##  [467,] 0.90445976 1.018537102
##  [468,] 0.84119661 1.385628660
##  [469,] 0.40325525 1.254264711
##  [470,] 2.09888097 1.278949849
##  [471,] 0.34927412 0.891238075
##  [472,] 0.74119094 0.265404867
##  [473,] 0.85170993 1.064592037
##  [474,] 1.35456943 1.355380547
##  [475,] 0.50335929 0.225230963
##  [476,] 1.00056864 1.171713105
##  [477,] 0.39278670 0.453869552
##  [478,] 0.45629123 1.067113952
##  [479,] 0.77340422 1.014750255
##  [480,] 0.46646960 0.688707314
##  [481,] 1.95385884 1.665489959
##  [482,] 0.78300579 0.840945617
##  [483,] 0.56689396 1.530712413
##  [484,] 1.93309644 1.567761634
##  [485,] 1.05572586 0.501965806
##  [486,] 1.65422785 1.775566071
##  [487,] 0.98790155 1.113385050
##  [488,] 0.71599647 1.600137393
##  [489,] 1.04272597 0.830269536
##  [490,] 1.68243281 1.577891753
##  [491,] 1.51228064 0.867866373
##  [492,] 0.34293241 1.081290012
##  [493,] 0.38404653 0.562482608
##  [494,] 0.64708102 0.829223898
##  [495,] 2.17362439 0.760215981
##  [496,] 0.56081100 0.740009010
##  [497,] 0.25493249 0.933352080
##  [498,] 0.58920355 1.731182516
##  [499,] 0.43312179 1.428431953
##  [500,] 0.80379847 1.157945330
##  [501,] 1.96809633 2.431203767
##  [502,] 1.17178144 0.907748942
##  [503,] 0.79933263 0.754133621
##  [504,] 1.85813593 1.474739166
##  [505,] 0.63763894 0.438803319
##  [506,] 0.78447850 0.760490576
##  [507,] 0.17790333 0.491024601
##  [508,] 0.36794554 1.390767940
##  [509,] 1.05164825 1.775679822
##  [510,] 1.95033499 0.248988677
##  [511,] 0.32571810 0.612763249
##  [512,] 1.92786897 0.286604524
##  [513,] 0.24402454 1.673326940
##  [514,] 0.86191048 1.640907372
##  [515,] 1.27906055 1.289389740
##  [516,] 0.77071934 1.700408412
##  [517,] 3.50778418 0.729671268
##  [518,] 0.57895933 0.682182545
##  [519,] 0.68172324 1.194024181
##  [520,] 1.23399138 0.533538879
##  [521,] 0.33995482 0.261685539
##  [522,] 1.58333302 1.191188018
##  [523,] 1.64433801 0.394147235
##  [524,] 0.96166464 1.126868132
##  [525,] 0.44417326 1.140224399
##  [526,] 0.65052055 0.860722406
##  [527,] 0.69913390 0.486933648
##  [528,] 0.76202417 0.583274409
##  [529,] 1.88180055 0.449216449
##  [530,] 0.74531930 0.910900585
##  [531,] 1.08673953 1.471285072
##  [532,] 0.79430262 2.075300181
##  [533,] 1.08655414 0.919696423
##  [534,] 0.64546192 1.884672193
##  [535,] 0.95854909 0.647101477
##  [536,] 0.83922476 0.901735224
##  [537,] 0.65416500 1.425562878
##  [538,] 1.38814150 0.280598151
##  [539,] 0.61639649 0.648731305
##  [540,] 1.06817446 0.455046858
##  [541,] 1.01941211 1.747387165
##  [542,] 1.01819185 0.351784678
##  [543,] 1.00532385 0.238505542
##  [544,] 0.21236340 1.745435034
##  [545,] 1.07580954 0.988529526
##  [546,] 0.53767324 0.832345096
##  [547,] 3.37457945 0.412869217
##  [548,] 1.30475447 0.250333619
##  [549,] 0.21683981 1.476141847
##  [550,] 0.58436281 1.395492649
##  [551,] 0.82854662 0.824639588
##  [552,] 0.87544482 0.594636222
##  [553,] 1.22566354 1.615690336
##  [554,] 1.91741564 0.566010399
##  [555,] 0.53494939 0.433522252
##  [556,] 0.49383414 1.755826746
##  [557,] 0.80800880 0.750080064
##  [558,] 0.97068530 0.845781209
##  [559,] 1.24181910 0.635029129
##  [560,] 0.38314543 0.808583395
##  [561,] 1.09555758 0.707232162
##  [562,] 1.23358509 0.382041407
##  [563,] 0.94597551 0.729855244
##  [564,] 0.63313250 0.538887958
##  [565,] 1.02069437 1.779410576
##  [566,] 0.86422208 1.351746875
##  [567,] 1.01131455 1.507926558
##  [568,] 0.35470317 1.379304024
##  [569,] 0.35882314 0.739395844
##  [570,] 1.27538822 0.341125610
##  [571,] 1.60858253 1.346632455
##  [572,] 0.44161767 1.911099570
##  [573,] 0.22907698 0.782039979
##  [574,] 0.68707755 0.796672816
##  [575,] 2.00125397 0.963974725
##  [576,] 1.21172140 1.511316993
##  [577,] 0.27481294 0.604981299
##  [578,] 0.86414691 0.406577694
##  [579,] 2.30959427 0.645145040
##  [580,] 1.09197548 0.388964581
##  [581,] 0.93435755 0.375728438
##  [582,] 0.21213346 1.275669044
##  [583,] 0.78403438 1.464354727
##  [584,] 0.51873530 1.035055131
##  [585,] 0.60215416 0.241282229
##  [586,] 0.86593004 2.444405668
##  [587,] 0.83034563 1.474461236
##  [588,] 0.68176904 2.478030328
##  [589,] 1.29513813 0.980613154
##  [590,] 0.75067189 0.366615677
##  [591,] 0.33832496 0.778034289
##  [592,] 0.95129147 0.527542325
##  [593,] 0.50517220 0.497840665
##  [594,] 0.42619495 0.814697092
##  [595,] 0.73722515 0.534718803
##  [596,] 0.74809202 0.663793515
##  [597,] 0.56998958 0.685131762
##  [598,] 0.51282265 0.774907958
##  [599,] 1.05484759 0.234353061
##  [600,] 0.54888193 0.940571205
##  [601,] 1.15574398 1.581713832
##  [602,] 1.33429747 0.619840467
##  [603,] 1.18240124 1.040315227
##  [604,] 0.38518834 0.664592347
##  [605,] 1.60830577 0.342015549
##  [606,] 1.48466222 0.479230257
##  [607,] 0.72512164 0.301099512
##  [608,] 0.89792910 1.323617587
##  [609,] 0.44984131 0.855564680
##  [610,] 0.81045275 0.521481691
##  [611,] 0.92866437 1.160735744
##  [612,] 1.41643262 0.449262190
##  [613,] 1.85084466 1.262719982
##  [614,] 1.63328106 0.951015570
##  [615,] 1.18521808 0.551421381
##  [616,] 1.58508709 1.624936544
##  [617,] 1.18856392 1.100518003
##  [618,] 0.43711357 1.043626778
##  [619,] 0.78874092 0.818719870
##  [620,] 1.04457873 0.536097755
##  [621,] 0.82592429 0.598467233
##  [622,] 0.90744738 2.182136086
##  [623,] 1.67530074 2.489381151
##  [624,] 0.79089384 0.596370552
##  [625,] 0.83663997 1.452746289
##  [626,] 0.55711833 1.519366989
##  [627,] 0.97731805 1.217221400
##  [628,] 0.72069576 0.168865752
##  [629,] 1.29863032 1.099578101
##  [630,] 0.90964788 1.184097549
##  [631,] 1.63339018 0.642958478
##  [632,] 1.19414790 0.619350677
##  [633,] 0.73073070 0.590891716
##  [634,] 0.35523664 0.448096266
##  [635,] 1.50815341 1.504014784
##  [636,] 0.80117830 1.456955102
##  [637,] 0.66045929 0.915348193
##  [638,] 1.86842198 1.390015247
##  [639,] 0.17540805 1.063617017
##  [640,] 0.64740281 1.183871512
##  [641,] 0.61684434 0.597962891
##  [642,] 1.41898118 0.842687760
##  [643,] 3.17826537 0.765613171
##  [644,] 0.86946392 0.859634641
##  [645,] 2.28914445 1.102224205
##  [646,] 2.94731255 1.273738033
##  [647,] 0.68703106 1.827279523
##  [648,] 1.21322259 1.707714243
##  [649,] 0.54690386 1.335263087
##  [650,] 2.66417673 1.462557386
##  [651,] 1.30676832 0.755528372
##  [652,] 0.52469436 1.945304453
##  [653,] 3.86173077 1.830407538
##  [654,] 1.18444809 0.435816918
##  [655,] 1.82125606 2.617005566
##  [656,] 0.19790057 0.523854850
##  [657,] 0.70422466 0.934002010
##  [658,] 1.19381733 0.696807512
##  [659,] 0.46017085 1.077844559
##  [660,] 0.49166720 0.535149795
##  [661,] 0.42765031 0.864401187
##  [662,] 3.53894419 0.265858185
##  [663,] 0.98693737 0.801352247
##  [664,] 1.49382127 2.041465929
##  [665,] 0.61080626 0.962745067
##  [666,] 2.80924718 0.114419097
##  [667,] 0.38081658 0.700526462
##  [668,] 2.35511039 1.590511472
##  [669,] 1.24111121 0.508660361
##  [670,] 0.89265876 2.114026060
##  [671,] 0.36783462 0.384634402
##  [672,] 0.80772536 1.553191107
##  [673,] 1.68809986 1.770857074
##  [674,] 0.76527208 0.664291053
##  [675,] 0.65042560 0.983895433
##  [676,] 2.21279937 2.256182960
##  [677,] 0.45132959 1.111522643
##  [678,] 1.21129480 1.491234795
##  [679,] 3.86029661 0.939579205
##  [680,] 0.53941227 0.538525807
##  [681,] 1.14802055 1.008733964
##  [682,] 0.69388371 0.773002614
##  [683,] 0.74815837 0.884456863
##  [684,] 1.02817493 0.406823245
##  [685,] 0.92598223 0.838030747
##  [686,] 0.78671274 1.055325006
##  [687,] 0.76740310 0.819601236
##  [688,] 1.47519178 1.306783010
##  [689,] 0.28879416 0.757153374
##  [690,] 0.49349823 0.918557704
##  [691,] 1.55463764 0.768794823
##  [692,] 1.54590316 0.995162094
##  [693,] 0.46659100 0.714231968
##  [694,] 0.62298735 1.168471924
##  [695,] 0.79984164 0.957905993
##  [696,] 0.69823892 1.566829130
##  [697,] 1.47776289 0.843541260
##  [698,] 1.26554627 1.051529957
##  [699,] 2.29228237 1.181286276
##  [700,] 0.57813712 1.102159393
##  [701,] 0.92949893 1.226139196
##  [702,] 1.29383506 0.667703532
##  [703,] 0.82642739 0.763494542
##  [704,] 1.51304866 1.042434795
##  [705,] 0.15720250 0.886484947
##  [706,] 1.21764429 1.109806532
##  [707,] 1.07673603 0.538353400
##  [708,] 0.78133022 0.701111494
##  [709,] 0.73945014 1.158065790
##  [710,] 0.48185453 0.797056925
##  [711,] 0.80255359 2.462794004
##  [712,] 0.48444344 0.506647296
##  [713,] 1.45240435 1.340167974
##  [714,] 0.31867188 0.933982311
##  [715,] 0.57157968 0.715218068
##  [716,] 0.44811540 0.654550608
##  [717,] 0.88625119 0.887138772
##  [718,] 0.90037483 0.703598962
##  [719,] 0.43808838 1.672990188
##  [720,] 0.65274042 1.591771926
##  [721,] 0.51914483 0.573659051
##  [722,] 0.96645381 0.886690786
##  [723,] 0.82185152 1.689822869
##  [724,] 1.20085730 0.993759308
##  [725,] 0.67746436 0.980658805
##  [726,] 0.70221970 0.675305483
##  [727,] 0.56914493 1.424074742
##  [728,] 0.54142720 0.287475909
##  [729,] 0.34522905 0.738983544
##  [730,] 0.28691538 0.823822344
##  [731,] 1.10196025 0.673946309
##  [732,] 1.96134238 0.744899690
##  [733,] 1.42694747 0.371913136
##  [734,] 1.11450657 0.931926742
##  [735,] 0.64267492 1.216285455
##  [736,] 0.11265274 0.658494476
##  [737,] 1.62368278 1.146288287
##  [738,] 1.14794272 1.318607873
##  [739,] 0.70395982 1.506289178
##  [740,] 0.42531375 0.327979241
##  [741,] 0.51550280 0.763256612
##  [742,] 0.80383533 0.725507021
##  [743,] 1.17506630 0.253464135
##  [744,] 2.14238048 1.605760058
##  [745,] 0.68083068 0.389817186
##  [746,] 1.22737174 1.070884271
##  [747,] 0.92454416 0.798308093
##  [748,] 0.58430427 0.530647786
##  [749,] 0.84740721 1.301859486
##  [750,] 0.44731215 0.601764718
##  [751,] 1.58314935 0.870996911
##  [752,] 0.40348286 0.581008939
##  [753,] 1.03110361 1.061115687
##  [754,] 1.75496135 0.750353549
##  [755,] 0.65935875 1.105800871
##  [756,] 1.52157572 0.650250059
##  [757,] 1.01046281 1.692003061
##  [758,] 0.43132005 0.898152553
##  [759,] 1.40747366 1.584099949
##  [760,] 0.35366270 0.483105117
##  [761,] 0.82385850 0.672143885
##  [762,] 0.69104532 1.086926498
##  [763,] 0.91782644 0.497329476
##  [764,] 0.77147637 1.378284014
##  [765,] 0.86071533 0.820852883
##  [766,] 0.49714206 0.532106404
##  [767,] 1.16875672 1.857008308
##  [768,] 0.57425543 1.183603046
##  [769,] 1.35047360 1.350757411
##  [770,] 1.15666508 0.151866535
##  [771,] 1.90769038 0.510204848
##  [772,] 1.09339788 0.772836609
##  [773,] 0.58019035 0.911516816
##  [774,] 0.25667812 0.518766215
##  [775,] 0.79117195 0.904268388
##  [776,] 0.94181564 1.359603145
##  [777,] 5.52518847 0.221073796
##  [778,] 0.68135300 1.696725260
##  [779,] 0.92245456 1.049484243
##  [780,] 1.68195247 0.930888273
##  [781,] 2.12004713 0.683446144
##  [782,] 0.94399667 0.798878475
##  [783,] 0.80970692 0.407977775
##  [784,] 0.44749460 0.762961195
##  [785,] 0.25953608 0.296056352
##  [786,] 0.32713801 0.733673194
##  [787,] 0.54218799 1.808531355
##  [788,] 2.28988886 1.332588124
##  [789,] 1.31679614 1.241637145
##  [790,] 0.16346977 1.178675548
##  [791,] 0.24150972 1.225104840
##  [792,] 0.79007722 0.759797427
##  [793,] 0.22274024 0.844680771
##  [794,] 0.30385244 0.233305839
##  [795,] 1.49557816 0.551533783
##  [796,] 0.52825890 0.920091772
##  [797,] 0.68527359 0.267664319
##  [798,] 0.45830871 1.292852689
##  [799,] 2.90123020 2.394361313
##  [800,] 0.86270874 1.882504752
##  [801,] 0.80525226 0.616197208
##  [802,] 0.31997388 1.170702585
##  [803,] 1.72132129 1.154298317
##  [804,] 1.16439418 0.531915886
##  [805,] 0.84010486 1.518254169
##  [806,] 0.96511560 0.944098878
##  [807,] 0.75463932 1.570759284
##  [808,] 1.25787354 0.308987239
##  [809,] 2.10763560 1.676883188
##  [810,] 1.25655583 0.771741523
##  [811,] 1.20149126 0.731191059
##  [812,] 0.53070646 0.769668920
##  [813,] 1.69905111 0.198984027
##  [814,] 2.52031926 1.324276646
##  [815,] 0.40835015 1.135312240
##  [816,] 0.93073208 0.546698241
##  [817,] 0.91087932 1.500447019
##  [818,] 0.70441165 0.263608647
##  [819,] 0.32905113 1.061831700
##  [820,] 0.66708075 0.382963821
##  [821,] 0.14945886 1.093420688
##  [822,] 2.75666456 0.158634585
##  [823,] 1.33993755 0.666622728
##  [824,] 1.17638970 0.708128558
##  [825,] 3.77553842 0.576286528
##  [826,] 0.89523937 0.542694884
##  [827,] 0.88153496 0.583358632
##  [828,] 1.00463222 0.970043484
##  [829,] 1.60291820 0.619380405
##  [830,] 0.29489239 0.975114041
##  [831,] 0.44772027 0.871559185
##  [832,] 0.59237202 0.724704578
##  [833,] 0.33830827 0.974996922
##  [834,] 0.57771522 0.894641996
##  [835,] 0.89862663 1.098393444
##  [836,] 1.49367706 0.116923718
##  [837,] 0.85707026 0.443766232
##  [838,] 1.66491824 1.303914743
##  [839,] 1.34132231 0.525003449
##  [840,] 0.94420586 2.379559590
##  [841,] 0.75064053 0.653922143
##  [842,] 0.75820232 1.091435802
##  [843,] 1.03625506 1.179135151
##  [844,] 0.67274508 1.681974599
##  [845,] 0.90813546 0.842629672
##  [846,] 1.01806207 1.448815858
##  [847,] 1.73529609 0.371176157
##  [848,] 1.26222111 1.488543811
##  [849,] 0.51716733 0.325703798
##  [850,] 0.97359801 0.704520483
##  [851,] 3.96758654 1.560948963
##  [852,] 0.41034869 0.796307923
##  [853,] 0.90399150 1.137231132
##  [854,] 1.14782493 1.510729383
##  [855,] 0.44503022 1.060149094
##  [856,] 0.47796841 0.556517255
##  [857,] 1.48282860 0.793160690
##  [858,] 1.36549478 0.865712171
##  [859,] 2.67102031 2.158056387
##  [860,] 0.70719133 0.243061677
##  [861,] 1.72482059 0.718642013
##  [862,] 0.36235592 0.453840089
##  [863,] 2.56210066 2.240706731
##  [864,] 0.55995507 0.998508563
##  [865,] 0.87893592 0.647022620
##  [866,] 0.90718386 0.295301729
##  [867,] 1.07992040 1.544006792
##  [868,] 0.59211841 0.800328122
##  [869,] 0.72841607 2.030364131
##  [870,] 2.05777125 0.757639295
##  [871,] 2.87808060 0.835113742
##  [872,] 1.26749428 0.566076485
##  [873,] 2.27317011 0.740802373
##  [874,] 1.29566331 1.040330032
##  [875,] 0.27534301 1.145961875
##  [876,] 1.21494590 0.620007632
##  [877,] 0.50013953 0.624180629
##  [878,] 0.93841010 1.225163545
##  [879,] 1.63438573 1.704152125
##  [880,] 1.80754685 1.427108281
##  [881,] 2.49556679 3.477827991
##  [882,] 1.25211336 0.131881464
##  [883,] 2.26317658 0.717512260
##  [884,] 0.42166616 0.646584241
##  [885,] 0.79539923 0.479127674
##  [886,] 1.66290424 0.448484401
##  [887,] 0.92286110 0.976964434
##  [888,] 0.20194136 0.623817267
##  [889,] 0.89278204 1.318955318
##  [890,] 0.78444176 0.289347397
##  [891,] 0.65463272 1.427884782
##  [892,] 1.41358014 3.052740899
##  [893,] 0.92392622 1.536152620
##  [894,] 0.17260471 0.961852235
##  [895,] 0.46317931 1.767607852
##  [896,] 0.27247005 0.913904269
##  [897,] 0.56690424 0.455747271
##  [898,] 0.44148609 1.221163421
##  [899,] 1.37089255 1.176935831
##  [900,] 0.76873569 1.238497297
##  [901,] 1.69307488 3.273560778
##  [902,] 0.59952479 0.248370190
##  [903,] 1.26545107 0.231434942
##  [904,] 0.89573753 0.820040162
##  [905,] 0.82149866 0.830034568
##  [906,] 0.29146458 0.994442107
##  [907,] 0.92161741 0.540857683
##  [908,] 0.82657083 1.130221193
##  [909,] 1.07260707 1.004319383
##  [910,] 0.93270484 2.844378759
##  [911,] 2.14962376 0.879296573
##  [912,] 1.31770177 0.414843430
##  [913,] 0.69593518 1.420558814
##  [914,] 0.69282340 1.951589954
##  [915,] 1.55937784 0.359919899
##  [916,] 2.55177865 0.608914782
##  [917,] 0.83913402 1.190552600
##  [918,] 0.80033774 0.806860962
##  [919,] 1.82864872 1.275365856
##  [920,] 1.08811604 0.579925761
##  [921,] 0.98781685 0.893113803
##  [922,] 0.54238893 1.612650122
##  [923,] 1.05293723 0.595826634
##  [924,] 0.83471490 1.491954192
##  [925,] 0.47256689 1.078259600
##  [926,] 1.49657778 0.718233202
##  [927,] 0.80602665 0.740200203
##  [928,] 0.29522740 0.694396450
##  [929,] 0.40266870 0.315911390
##  [930,] 1.09114637 0.858224900
##  [931,] 0.50825096 1.089501831
##  [932,] 0.16597464 1.299739114
##  [933,] 0.69880328 1.282196119
##  [934,] 0.89780478 1.344691195
##  [935,] 0.75788250 1.150674192
##  [936,] 0.94001244 0.292282395
##  [937,] 1.16333149 0.980252516
##  [938,] 1.84294772 0.824957238
##  [939,] 0.26372511 1.033409427
##  [940,] 1.01112672 0.532863059
##  [941,] 1.49115404 1.154852125
##  [942,] 0.57814286 0.729939942
##  [943,] 0.68738150 0.912512192
##  [944,] 0.63402394 0.592203205
##  [945,] 0.59287468 0.942758912
##  [946,] 0.20319084 0.332591393
##  [947,] 0.36511823 0.232451157
##  [948,] 0.36432500 0.290728993
##  [949,] 1.00328199 1.223967961
##  [950,] 0.83878346 0.574566600
##  [951,] 0.80452490 1.233056641
##  [952,] 0.43636043 0.452254133
##  [953,] 2.95946160 1.713495305
##  [954,] 0.70927671 0.914937445
##  [955,] 0.87313051 1.583903839
##  [956,] 0.27211123 0.397220475
##  [957,] 0.59841670 0.436699228
##  [958,] 2.22848411 0.592353639
##  [959,] 0.80391666 1.719901680
##  [960,] 0.82339076 1.511086453
##  [961,] 0.56146826 0.204092097
##  [962,] 0.57905695 0.624537542
##  [963,] 0.91953409 0.767203783
##  [964,] 1.12158030 3.794498035
##  [965,] 0.47249768 1.359916098
##  [966,] 0.41982676 2.446763641
##  [967,] 1.33098810 1.784839617
##  [968,] 0.80076476 0.859812457
##  [969,] 0.80434215 0.901188487
##  [970,] 0.50037988 0.749066362
##  [971,] 0.65788204 1.205801096
##  [972,] 1.17092973 1.401353931
##  [973,] 0.74525667 1.289981407
##  [974,] 1.10183139 0.679747295
##  [975,] 0.52289264 1.001014066
##  [976,] 0.33580336 0.481234523
##  [977,] 1.78442880 2.798897738
##  [978,] 0.51141648 1.097367186
##  [979,] 0.34620161 0.846713273
##  [980,] 0.33394149 0.225208232
##  [981,] 0.70380781 1.117636144
##  [982,] 1.01154058 3.097295097
##  [983,] 3.31542666 1.521215716
##  [984,] 0.41733718 0.433503284
##  [985,] 0.48217266 1.288759019
##  [986,] 0.89866837 0.714814256
##  [987,] 0.72729241 0.529683915
##  [988,] 1.18292344 2.953227145
##  [989,] 1.53020639 0.332466765
##  [990,] 0.94141883 0.892244690
##  [991,] 2.51454734 3.686478225
##  [992,] 1.59313983 0.856957474
##  [993,] 0.72755285 1.418979712
##  [994,] 0.44822243 0.797848194
##  [995,] 0.91740605 0.421418312
##  [996,] 0.70963245 1.053679065
##  [997,] 0.61577238 1.991289185
##  [998,] 0.23909102 1.782428051
##  [999,] 0.75763838 0.616216765
## 
## $model.matrix
##    (Intercept) microsite1 shrub_density
## 1            1          1            11
## 2            1          1            12
## 3            1         -1             0
## 4            1         -1             0
## 5            1          1            11
## 6            1          1            10
## 7            1         -1             0
## 8            1         -1             0
## 9            1          1            14
## 10           1          1            13
## 11           1         -1             0
## 12           1         -1             0
## 13           1          1            11
## 14           1          1            11
## 15           1         -1             0
## 16           1         -1             0
## 17           1          1            10
## 18           1          1            11
## 19           1          1            11
## 20           1          1            10
## 21           1         -1             0
## 22           1         -1             0
## 
## $terms
## pca_data ~ microsite * shrub_density
## attr(,"variables")
## list(pca_data, microsite, shrub_density)
## attr(,"factors")
##               microsite shrub_density microsite:shrub_density
## pca_data              0             0                       0
## microsite             1             0                       1
## shrub_density         0             1                       1
## attr(,"term.labels")
## [1] "microsite"               "shrub_density"          
## [3] "microsite:shrub_density"
## attr(,"order")
## [1] 1 1 2
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## attr(,"class")
## [1] "adonis"
dist <- vegdist(pca_data, species = "bray")
res <- pcoa(dist)
p1 <- as.data.frame(res$vectors)%>%
  dplyr::select(Axis.1, Axis.2) %>%
  bind_cols(env,.)

ggplot(p1, aes(Axis.1, Axis.2, group = microsite)) +
  geom_point(aes(color = microsite)) +
  geom_text(aes(label=plot), hjust = 0, vjust = 0, check_overlap = TRUE, nudge_x = 0.01)+
  scale_color_brewer(palette = "Set1") +
  labs(color = "", subtitle = "labels denote plot identity")

m02 <- betadisper(dist, env$microsite)
m02
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist, group = env$microsite)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
## Density    Open 
##  0.5063  0.4721 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 21 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.4339 1.1869 0.9571 0.4725 0.4027 0.3112 0.1809 0.1156
anova(m02)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq F value Pr(>F)
## Groups     1 0.00638 0.006378  0.1212 0.7313
## Residuals 20 1.05203 0.052602
permutest(m02,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq      F N.Perm Pr(>F)
## Groups     1 0.00638 0.006378 0.1212     99   0.74
## Residuals 20 1.05203 0.052602                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##         Density Open
## Density         0.72
## Open    0.73133
m02.HSD <- TukeyHSD(m02)
boxplot(m02)

m03 <- betadisper(dist, env$shrub_density)
m03
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist, group = env$shrub_density)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
##      0     10     11     12     13     14 
## 0.4721 0.5171 0.4968 0.0000 0.0000 0.0000 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 21 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.4339 1.1869 0.9571 0.4725 0.4027 0.3112 0.1809 0.1156
anova(m03)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq Mean Sq F value  Pr(>F)  
## Groups     5 0.61999 0.12400  2.3507 0.08827 .
## Residuals 16 0.84400 0.05275                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(m03,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq Mean Sq      F N.Perm Pr(>F)  
## Groups     5 0.61999 0.12400 2.3507     99   0.09 .
## Residuals 16 0.84400 0.05275                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##          0      10      11 12 13 14
## 0          0.76000 0.80000         
## 10 0.76968         0.89000         
## 11 0.84659 0.89212                 
## 12                                 
## 13                                 
## 14
m03.HSD <- TukeyHSD(m03)
boxplot(m03)

m04 <- betadisper(dist, env$site)
m04
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist, group = env$site)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
## Carrizo  Cuyama  Tecopa 
##  0.2828  0.3427  0.4625 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 21 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.4339 1.1869 0.9571 0.4725 0.4027 0.3112 0.1809 0.1156
anova(m04)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq F value Pr(>F)
## Groups     2 0.11217 0.056087  1.1941 0.3247
## Residuals 19 0.89240 0.046969
permutest(m04,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq      F N.Perm Pr(>F)
## Groups     2 0.11217 0.056087 1.1941     99   0.37
## Residuals 19 0.89240 0.046969                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##         Carrizo  Cuyama Tecopa
## Carrizo         0.61000   0.20
## Cuyama  0.54695           0.32
## Tecopa  0.19772 0.31784
m04.HSD <- TukeyHSD(m04)
boxplot(m04)

### 2023 Data

photo_2023 <- read.csv("observations_2023.csv")
summary(photo_2023)
##     region              site            site_code          microsite        
##  Length:192701      Length:192701      Length:192701      Length:192701     
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##       plot           cam_ID        month               date          
##  Min.   :1.000   Min.   :1.00   Length:192701      Length:192701     
##  1st Qu.:1.000   1st Qu.:1.00   Class :character   Class :character  
##  Median :2.000   Median :1.00   Mode  :character   Mode  :character  
##  Mean   :1.771   Mean   :1.49                                        
##  3rd Qu.:2.000   3rd Qu.:2.00                                        
##  Max.   :4.000   Max.   :2.00                                        
##       year      shrub_density         rep         identified_by     
##  Min.   :2023   Min.   : 0.000   Min.   :     1   Length:192701     
##  1st Qu.:2023   1st Qu.: 0.000   1st Qu.: 48176   Class :character  
##  Median :2023   Median :10.000   Median : 96351   Mode  :character  
##  Mean   :2023   Mean   : 6.239   Mean   : 96351                     
##  3rd Qu.:2023   3rd Qu.:11.000   3rd Qu.:144526                     
##  Max.   :2023   Max.   :14.000   Max.   :192701                     
##    filename          timestamp           animal.hit          class          
##  Length:192701      Length:192701      Min.   :0.000000   Length:192701     
##  Class :character   Class :character   1st Qu.:0.000000   Class :character  
##  Mode  :character   Mode  :character   Median :0.000000   Mode  :character  
##                                        Mean   :0.005392                     
##                                        3rd Qu.:0.000000                     
##                                        Max.   :1.000000                     
##     order              family             genus             species         
##  Length:192701      Length:192701      Length:192701      Length:192701     
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  common_name        number_of_objects
##  Length:192701      Min.   :1        
##  Class :character   1st Qu.:1        
##  Mode  :character   Median :1        
##                     Mean   :1        
##                     3rd Qu.:1        
##                     Max.   :2
photo_2023 <- photo_2023 %>%
  filter(common_name != "Human")
photo_2023 <- photo_2023 %>%
  filter(common_name != "Human-Camera Trapper")
photo_2023 <- photo_2023 %>%
  filter(common_name != "Domestic Dog")
photo_2023 <- photo_2023 %>%
  filter(common_name != "Vehicle")
photo_2023 <- photo_2023 %>%
  dplyr::filter(common_name != "Insect")
photo_2023 <- photo_2023 %>%
  dplyr::filter(common_name != "Animal")
photo_2023 <- photo_2023 %>%
  dplyr::filter(common_name != "Bird")
photo_2023 <- photo_2023 %>%
  dplyr::filter(common_name != "No CV Result")
  
count.hit_2023 <- photo_2023 %>%
  count(animal.hit) %>%
  na.omit()
summary(count.hit_2023)
##    animal.hit         n         
##  Min.   :0.00   Min.   :   546  
##  1st Qu.:0.25   1st Qu.: 48325  
##  Median :0.50   Median : 96104  
##  Mean   :0.50   Mean   : 96104  
##  3rd Qu.:0.75   3rd Qu.:143883  
##  Max.   :1.00   Max.   :191662
### 2023 had a 0.28% capture rate
### Animal Observations by Site_Code
animals_by_sitecode_2023 <- photo_2023%>%
  group_by(site_code, microsite, common_name) %>%
  summarise(captures = sum(animal.hit), n = n())
## `summarise()` has grouped output by 'site_code', 'microsite'. You can override
## using the `.groups` argument.
animals_by_sitecode_2023 <- animals_by_sitecode_2023 %>%
  filter(common_name != "Blank") %>% filter(common_name != "No CV Result") 
### Animal observations by Site 2023
animals_by_site_2023 <- photo_2023 %>% group_by(site,microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site', 'microsite'. You can override using
## the `.groups` argument.
animals_by_site_2023 <- animals_by_site_2023 %>% filter(common_name != "Blank") %>% filter(common_name != "No CV Result") 
### Animal observations by Density
animals_by_density_2023 <- photo_2023 %>% group_by(microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'microsite'. You can override using the
## `.groups` argument.
animals_by_density_2023 <- animals_by_density_2023 %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result")
### Total Observations 2023
Total_Observations_2023 <- photo_2023 %>% group_by(common_name) %>% summarise(total = sum(animal.hit)) %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result")
density_obvs_2023 <- merge(animals_by_density_2023, Total_Observations_2023, all = TRUE)
density_obvs_2023$percent_presence <- density_obvs_2023$captures/density_obvs_2023$total
### Percent proportion Figure
plot2 <- ggplot(density_obvs_2023, aes(common_name, percent_presence, fill = microsite)) + geom_bar(stat = "identity") + coord_flip() + theme_classic() + scale_x_discrete(limits=rev) + xlab("Species") + ylab("Percent Proportion") + labs(fill = "Microsite")
plot2 + scale_fill_manual(values = c("#009900", "#0066cc"))

m2<- glm(total ~ microsite*common_name, family = "poisson", data = density_obvs_2023)
anova(m2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: total
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                                     37     2413.4             
## microsite              1     89.8        36     2323.6   <2e-16 ***
## common_name           24   2323.6        12        0.0   <2e-16 ***
## microsite:common_name 12      0.0         0        0.0        1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e2 <- emmeans(m2, pairwise~common_name)
## NOTE: Results may be misleading due to involvement in interactions
#head(e2)
animals_density_2023 <- photo_2023 %>% group_by(site_code,microsite,plot, shrub_density, common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site_code', 'microsite', 'plot',
## 'shrub_density'. You can override using the `.groups` argument.
animals_density_2023 <- animals_density_2023 %>% filter(common_name != "Blank")
pca_data_2023 <- animals_density_2023 ### Created new df for pcoa data
pca_data_2023 <- pca_data_2023 %>%
  spread(common_name, captures) %>%
  ungroup() %>%
  dplyr::select(-site_code, -microsite, -plot) %>%
  replace(is.na(.),0)
dim(pca_data_2023)
## [1] 23 26
env_2023 <- read.csv("environment_2023.csv") ### Drop Tecopa open 1, Tecopa open 4, since they have no animal observations.
dim(env)
## [1] 22  5
model01 <- adonis(pca_data_2023 ~ microsite*shrub_density, data = env_2023)
## 'adonis' will be deprecated: use 'adonis2' instead
model01
## $aov.tab
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##               Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
## microsite      1    0.4511 0.45114  1.6082 0.06930  0.129
## shrub_density  1    0.4482 0.44823  1.5978 0.06885  0.124
## Residuals     20    5.6105 0.28052         0.86184       
## Total         22    6.5099                 1.00000       
## 
## $call
## adonis(formula = pca_data_2023 ~ microsite * shrub_density, data = env_2023)
## 
## $coefficients
##                          shrub_density Black-tailed Jackrabbit
## (Intercept)                 -10.398601               2.8438228
## microsite1                  -14.216783              -3.7925408
## shrub_density                 2.876923               0.4769231
## microsite1:shrub_density            NA                      NA
##                          Black-throated Sparrow Blunt-nosed Leopard Lizard
## (Intercept)                        4.545455e-02                 0.12820513
## microsite1                        -4.545455e-02                 0.12820513
## shrub_density                     -6.331379e-18                -0.01538462
## microsite1:shrub_density                     NA                         NA
##                          Brewer's Blackbird California Ground Squirrel
## (Intercept)                      -2.5571096                -0.21794872
## microsite1                       -2.6480186                -0.21794872
## shrub_density                     0.4923077                 0.04615385
## microsite1:shrub_density                 NA                         NA
##                          California Quail California Thrasher Common Raven
## (Intercept)                    -1.8205128          0.47435897    2.6340326
## microsite1                     -1.8205128          0.47435897    1.7249417
## shrub_density                   0.3384615         -0.07692308   -0.2615385
## microsite1:shrub_density               NA                  NA           NA
##                             Coyote Desert Cottontail Desert Iguana
## (Intercept)               3.060606        -2.3391608  4.545455e-02
## microsite1                1.606061        -2.4300699 -4.545455e-02
## shrub_density            -0.200000         0.4461538  8.356568e-18
## microsite1:shrub_density        NA                NA            NA
##                          Giant Kangaroo Rat Heermann's Kangaroo Rat Horned Lark
## (Intercept)                      0.03263403               -7.849650  0.38461538
## microsite1                      -0.05827506              -15.304196  0.38461538
## shrub_density                    0.06153846                3.169231 -0.04615385
## microsite1:shrub_density                 NA                      NA          NA
##                             Kit Fox Lizards and Snakes Loggerhead Shrike
## (Intercept)               2.1165501       2.727273e-01        -0.4801865
## microsite1                1.9347319      -2.727273e-01        -0.5710956
## shrub_density            -0.3230769      -1.513076e-17         0.1230769
## microsite1:shrub_density         NA                 NA                NA
##                               Mammal Merriam's Kangaroo Rat
## (Intercept)              -0.21794872             1.10256410
## microsite1               -0.21794872             0.10256410
## shrub_density             0.04615385            -0.09230769
## microsite1:shrub_density          NA                     NA
##                          Nelson's Antelope Squirrel Salinas Pocket Mouse
## (Intercept)                               0.3694639          -0.39044289
## microsite1                               -0.2668998          -0.48135198
## shrub_density                             0.1538462           0.09230769
## microsite1:shrub_density                         NA                   NA
##                          Say's Phoebe Vesper Sparrow Western whiptail
## (Intercept)               0.264568765      1.5384615       0.12820513
## microsite1               -0.008158508      1.5384615       0.12820513
## shrub_density            -0.015384615     -0.1846154      -0.01538462
## microsite1:shrub_density           NA             NA               NA
##                          White-tailed Antelope Squirrel
## (Intercept)                                  0.35547786
## microsite1                                  -0.09906760
## shrub_density                               -0.01538462
## microsite1:shrub_density                             NA
## 
## $coef.sites
##                                    1           2           3           4
## (Intercept)               1.08713373  1.19242360  1.04021622  0.53368864
## microsite1                0.27702067  0.36812565  0.28650205 -0.08921598
## shrub_density            -0.05750503 -0.07418322 -0.03323392  0.02592824
## microsite1:shrub_density          NA          NA          NA          NA
##                                    5            6          7           8
## (Intercept)               1.09169046  0.725232927  0.9149049  0.73036046
## microsite1                0.43517627 -0.003397368  0.1285966 -0.03557956
## shrub_density            -0.08696283 -0.012927632 -0.0247195  0.01666357
## microsite1:shrub_density          NA           NA         NA          NA
##                                   9         10          11          12
## (Intercept)               1.3003752  1.4998669  0.80294716  0.64129703
## microsite1                0.6190745  0.7936762  0.05159731 -0.03324735
## shrub_density            -0.1227435 -0.1491194 -0.01154984  0.01898538
## microsite1:shrub_density         NA         NA          NA          NA
##                                   13          14          15          16
## (Intercept)               0.99239018  0.66809163  0.63858697 -0.08681298
## microsite1                0.34039631 -0.04876636 -0.21003546 -0.87304773
## shrub_density            -0.06950611 -0.01035118  0.04254088  0.14042524
## microsite1:shrub_density          NA          NA          NA          NA
##                                   17         18          19          20
## (Intercept)               0.17811261  0.1694050 -0.01538676  0.91285079
## microsite1               -0.64882951 -0.6891926 -0.81989153  0.22319732
## shrub_density             0.09926822  0.1072032  0.13358216 -0.04137692
## microsite1:shrub_density          NA         NA          NA          NA
##                                   21          22         23
## (Intercept)               0.95345668  1.13091299  0.9134932
## microsite1                0.30456994  0.48161788  0.2756840
## shrub_density            -0.05633216 -0.08893335 -0.0522899
## microsite1:shrub_density          NA          NA         NA
## 
## $f.perms
##              [,1]      [,2]
##    [1,] 2.7382748 0.7171803
##    [2,] 1.0996783 1.4344806
##    [3,] 2.3782813 0.8155126
##    [4,] 0.8280660 0.4049624
##    [5,] 0.7374631 1.0327982
##    [6,] 0.5944951 0.4515525
##    [7,] 0.2700776 1.8120483
##    [8,] 1.6040864 1.2528508
##    [9,] 0.3660925 2.0217544
##   [10,] 1.0117398 1.7981395
##   [11,] 0.9781887 2.1096450
##   [12,] 0.3537379 0.3642225
##   [13,] 0.6869765 0.6567368
##   [14,] 0.3115720 2.1928635
##   [15,] 1.7331453 1.0169350
##   [16,] 0.9596079 0.9861569
##   [17,] 1.8406550 0.4119059
##   [18,] 0.3954707 1.0367186
##   [19,] 0.4924088 1.2389746
##   [20,] 1.0030954 0.6866150
##   [21,] 1.0640408 0.6412791
##   [22,] 0.9843796 0.3781761
##   [23,] 0.7182460 0.9079104
##   [24,] 0.6055968 0.8098724
##   [25,] 0.2824401 0.6837748
##   [26,] 0.5465991 1.1281813
##   [27,] 0.9923677 0.9763268
##   [28,] 1.6439075 2.2489744
##   [29,] 1.5983089 1.0626882
##   [30,] 0.3395985 0.2210830
##   [31,] 0.5354982 1.0033802
##   [32,] 0.4518611 1.0375600
##   [33,] 0.9156338 0.6945022
##   [34,] 0.7326711 0.8719917
##   [35,] 1.3270950 1.1630793
##   [36,] 0.8555655 0.5909281
##   [37,] 1.1364610 1.9181392
##   [38,] 0.9847799 1.1672615
##   [39,] 0.6691929 1.2085231
##   [40,] 1.0459579 1.4759968
##   [41,] 1.0358562 0.8281517
##   [42,] 0.1351022 0.7852149
##   [43,] 2.1573028 1.0567682
##   [44,] 1.2066674 0.5195105
##   [45,] 0.7119275 1.1815594
##   [46,] 1.3999410 0.8208377
##   [47,] 0.8715805 0.4762804
##   [48,] 1.0036517 0.3713635
##   [49,] 0.9013351 1.1669415
##   [50,] 0.7913610 1.3989553
##   [51,] 0.8824895 1.3064191
##   [52,] 1.5838122 0.3706992
##   [53,] 0.4668202 0.5556006
##   [54,] 1.3747239 0.7677864
##   [55,] 0.7102356 0.7489866
##   [56,] 1.1258842 0.9371586
##   [57,] 0.7633517 1.4325719
##   [58,] 1.0539526 0.8244041
##   [59,] 0.7733155 0.5959915
##   [60,] 2.1202396 1.2558250
##   [61,] 0.4000565 0.6605348
##   [62,] 0.7346400 0.7047121
##   [63,] 0.5636768 0.4251710
##   [64,] 1.3602660 0.9158437
##   [65,] 3.5742708 1.1446878
##   [66,] 0.5392069 1.0717975
##   [67,] 1.0402897 2.7969678
##   [68,] 0.8564135 0.9154163
##   [69,] 1.3147426 1.0918524
##   [70,] 1.0151126 0.8037166
##   [71,] 2.6822804 1.0277958
##   [72,] 0.8316963 1.2658315
##   [73,] 3.1110483 1.5605846
##   [74,] 0.7861471 0.6792935
##   [75,] 0.8190844 0.2677384
##   [76,] 1.4115869 0.8721571
##   [77,] 0.4187621 1.5049565
##   [78,] 1.3344876 1.4396763
##   [79,] 0.8082365 0.3968630
##   [80,] 1.6092280 2.4011541
##   [81,] 0.6209134 0.7288840
##   [82,] 1.5338524 0.7781797
##   [83,] 0.4463297 1.3301870
##   [84,] 0.5014001 1.6453936
##   [85,] 2.1915007 0.4617612
##   [86,] 0.1755958 1.2038608
##   [87,] 0.9807270 1.7546097
##   [88,] 1.0925057 0.5535764
##   [89,] 1.1285489 0.9410264
##   [90,] 1.3845553 1.0935328
##   [91,] 0.8005270 0.8543149
##   [92,] 1.7747441 0.8148711
##   [93,] 0.9656347 0.8850079
##   [94,] 0.6724260 0.9625644
##   [95,] 0.2211525 0.8763503
##   [96,] 0.9643899 0.9209384
##   [97,] 0.2984458 0.5916444
##   [98,] 0.8318393 1.0643771
##   [99,] 0.3485737 0.5600867
##  [100,] 1.4211614 0.5178163
##  [101,] 0.8369026 1.5334397
##  [102,] 0.9811977 1.2179178
##  [103,] 1.6022900 0.7091963
##  [104,] 0.5926428 0.4787760
##  [105,] 0.7038819 1.8297473
##  [106,] 0.6762639 0.1467004
##  [107,] 0.9063436 0.6218488
##  [108,] 0.7048776 1.2205993
##  [109,] 1.0545086 0.3796934
##  [110,] 0.3046786 0.5413877
##  [111,] 1.0339587 0.7049948
##  [112,] 0.6323795 1.2105481
##  [113,] 0.8595198 0.6784251
##  [114,] 0.4045428 0.4594704
##  [115,] 0.7212456 1.2271784
##  [116,] 0.5415000 0.7366891
##  [117,] 0.7969268 0.8390085
##  [118,] 0.7309664 0.7818723
##  [119,] 1.1482505 1.4215844
##  [120,] 1.3587255 1.5311380
##  [121,] 1.3841010 1.5219691
##  [122,] 0.3496842 1.5392874
##  [123,] 0.9228000 0.3786625
##  [124,] 0.7945953 1.9580517
##  [125,] 0.8799227 1.0240600
##  [126,] 1.5267668 0.5968688
##  [127,] 0.6450349 1.5959289
##  [128,] 1.3204904 2.2284481
##  [129,] 0.4517017 0.2286479
##  [130,] 1.7248174 2.2161323
##  [131,] 0.5792634 0.4573465
##  [132,] 0.2539590 0.4914602
##  [133,] 0.9787231 1.3675160
##  [134,] 2.0534593 1.8354910
##  [135,] 0.8936060 1.2910296
##  [136,] 1.1117847 1.1632545
##  [137,] 0.7230107 0.6297134
##  [138,] 0.4846413 0.7945592
##  [139,] 0.5727237 0.5243089
##  [140,] 0.3890955 0.5364520
##  [141,] 1.5884495 0.4146156
##  [142,] 1.6719877 1.2796764
##  [143,] 0.7227712 1.4025224
##  [144,] 1.6980909 1.0824444
##  [145,] 0.8471497 0.7650705
##  [146,] 0.7701617 0.7934832
##  [147,] 0.4243351 0.8323766
##  [148,] 1.0581203 2.0158779
##  [149,] 1.4292932 1.0927163
##  [150,] 1.5770383 0.7831433
##  [151,] 0.4843029 2.5750417
##  [152,] 2.3321275 1.4589910
##  [153,] 0.9541153 1.4787789
##  [154,] 0.8462835 1.0951974
##  [155,] 0.4845349 0.5057734
##  [156,] 0.4447651 0.5497398
##  [157,] 1.4249147 1.4249616
##  [158,] 0.8641810 0.5353499
##  [159,] 0.7535915 1.4157121
##  [160,] 0.7211604 1.7423315
##  [161,] 1.6697859 1.0926917
##  [162,] 0.4850397 1.0495755
##  [163,] 0.9494819 1.0830195
##  [164,] 0.5013202 0.3453050
##  [165,] 1.4455322 1.4107392
##  [166,] 0.4575864 1.0590453
##  [167,] 0.8587519 0.9189470
##  [168,] 1.7314059 0.5817640
##  [169,] 1.1446649 1.2892957
##  [170,] 0.1944590 0.4050381
##  [171,] 1.0248612 0.9545152
##  [172,] 1.7270129 1.7498332
##  [173,] 0.6096415 0.2546216
##  [174,] 0.8369686 0.6958042
##  [175,] 0.4132246 0.8197026
##  [176,] 0.3661891 1.0796383
##  [177,] 0.6077763 1.0529853
##  [178,] 1.0715529 1.0561281
##  [179,] 1.7001175 0.7091150
##  [180,] 0.7361720 0.8475822
##  [181,] 0.8762563 1.0379011
##  [182,] 1.2684685 1.1919251
##  [183,] 0.4276396 1.2611834
##  [184,] 2.8355078 0.9993001
##  [185,] 0.7768380 1.2091902
##  [186,] 0.2092950 1.0856551
##  [187,] 0.8358542 1.8473285
##  [188,] 0.4156293 1.2109307
##  [189,] 0.3714976 0.7367634
##  [190,] 1.4092837 0.8752986
##  [191,] 2.8103818 1.5931489
##  [192,] 0.4381570 0.9683500
##  [193,] 0.6628551 1.4338904
##  [194,] 1.3559238 0.5258778
##  [195,] 1.0831014 0.4337764
##  [196,] 0.7431218 1.5546510
##  [197,] 0.7119704 0.7677798
##  [198,] 0.6519377 1.2742883
##  [199,] 1.6637430 1.7226449
##  [200,] 0.7407142 1.9124531
##  [201,] 2.3250093 0.7669119
##  [202,] 0.6430732 1.4264210
##  [203,] 0.2251508 0.7628526
##  [204,] 0.7382890 1.7471426
##  [205,] 0.7358557 1.8307957
##  [206,] 1.1976856 0.1871336
##  [207,] 1.3850117 1.5236655
##  [208,] 3.6285246 0.1543495
##  [209,] 2.3378367 1.2511940
##  [210,] 0.7502639 1.0607068
##  [211,] 0.2650657 0.9638570
##  [212,] 0.5112553 0.8759559
##  [213,] 0.2517901 0.5253464
##  [214,] 0.4581573 0.4394306
##  [215,] 0.8427951 1.1174081
##  [216,] 1.1153856 1.2496810
##  [217,] 0.3470439 0.5384574
##  [218,] 1.5227470 0.2661442
##  [219,] 0.2857581 0.2988910
##  [220,] 1.8345692 0.8002780
##  [221,] 2.2925783 0.6880305
##  [222,] 1.8603672 0.4334282
##  [223,] 0.3514318 0.9948148
##  [224,] 0.2356391 1.4956580
##  [225,] 0.3359739 0.6465703
##  [226,] 0.4565029 0.6570457
##  [227,] 0.5302350 0.4076297
##  [228,] 2.0858830 0.8999596
##  [229,] 1.4188408 1.3344929
##  [230,] 0.3673561 1.5636543
##  [231,] 0.2791463 3.1029927
##  [232,] 0.3546264 1.3718738
##  [233,] 1.1841830 1.7188711
##  [234,] 0.5696267 0.3225966
##  [235,] 0.6446204 1.7212909
##  [236,] 0.9964268 1.1447857
##  [237,] 0.5819861 1.2944011
##  [238,] 0.7586545 1.1107310
##  [239,] 1.1608977 1.5863768
##  [240,] 1.1139159 0.4311611
##  [241,] 1.5933132 2.2439207
##  [242,] 0.2466766 0.8765495
##  [243,] 0.5680325 0.5677540
##  [244,] 0.6651244 0.9780343
##  [245,] 1.4956913 1.0424931
##  [246,] 0.9080724 0.9065774
##  [247,] 3.9122141 0.6313720
##  [248,] 0.8140993 0.2937924
##  [249,] 0.9413952 0.3314775
##  [250,] 1.3960193 1.0693777
##  [251,] 0.5760652 0.4599618
##  [252,] 0.6524602 1.1545962
##  [253,] 1.2972066 0.6867424
##  [254,] 1.1580809 2.5431738
##  [255,] 1.0689786 0.5396955
##  [256,] 0.3988668 0.7267875
##  [257,] 4.6210976 1.4304686
##  [258,] 0.5056060 0.9293644
##  [259,] 0.2941735 1.4407908
##  [260,] 0.4228639 0.3986348
##  [261,] 0.7656118 1.0174922
##  [262,] 1.0252028 0.8698664
##  [263,] 0.9210359 0.4020360
##  [264,] 2.1080268 0.6316757
##  [265,] 0.4946632 0.2409981
##  [266,] 1.0298644 0.6655478
##  [267,] 0.6493145 1.1558696
##  [268,] 0.5064393 0.4709991
##  [269,] 1.3458163 0.5401089
##  [270,] 1.4851297 0.9861983
##  [271,] 0.9054266 0.9766538
##  [272,] 0.8164144 1.0705109
##  [273,] 1.3866390 2.1130757
##  [274,] 1.8725633 0.3893257
##  [275,] 2.0932749 2.6145556
##  [276,] 2.3908334 2.1623106
##  [277,] 0.8773963 0.5352939
##  [278,] 0.5445651 0.4592441
##  [279,] 0.9107882 1.9901383
##  [280,] 2.7385027 0.6858667
##  [281,] 0.8146993 1.0554619
##  [282,] 1.1975190 2.1243922
##  [283,] 0.6178906 1.0333659
##  [284,] 0.6572143 1.2588776
##  [285,] 1.7802869 0.5759819
##  [286,] 2.1121769 0.9731656
##  [287,] 0.9594241 1.3242740
##  [288,] 0.4952664 0.9200930
##  [289,] 1.0426448 0.9538543
##  [290,] 0.8094580 0.4960585
##  [291,] 0.4842182 0.7224853
##  [292,] 1.4881907 1.3101465
##  [293,] 0.3966110 0.4669428
##  [294,] 0.4897662 1.3048950
##  [295,] 0.7885785 0.9826327
##  [296,] 0.7531094 0.4659524
##  [297,] 0.3063564 1.2092907
##  [298,] 1.3730312 0.6836954
##  [299,] 0.6925015 0.9115949
##  [300,] 0.4270587 1.4444938
##  [301,] 0.4082033 0.1213776
##  [302,] 0.1604592 0.6832453
##  [303,] 0.6018508 0.5553902
##  [304,] 0.9910496 1.3576774
##  [305,] 2.0718793 0.5926211
##  [306,] 0.7382321 0.5368768
##  [307,] 1.4002611 0.6849764
##  [308,] 1.1115770 0.4098753
##  [309,] 1.0428577 0.4924156
##  [310,] 0.9324888 0.3729700
##  [311,] 0.8338924 0.6785926
##  [312,] 0.3913868 0.2980295
##  [313,] 1.2065072 0.4845828
##  [314,] 0.4531253 0.7202862
##  [315,] 0.3784645 1.3980201
##  [316,] 1.2713628 1.1180881
##  [317,] 0.7964369 1.1614769
##  [318,] 0.4842959 0.4703779
##  [319,] 0.5268028 1.9978255
##  [320,] 0.7830322 0.8073375
##  [321,] 1.0789229 0.6171273
##  [322,] 0.6362473 0.4517443
##  [323,] 0.6067322 1.1907439
##  [324,] 1.3817046 1.6007422
##  [325,] 0.7411202 0.7598022
##  [326,] 0.9900606 0.5363007
##  [327,] 0.8222969 1.4542447
##  [328,] 0.8504734 0.5263582
##  [329,] 3.7126051 2.5084904
##  [330,] 0.5570236 0.1803003
##  [331,] 0.2512155 1.6901621
##  [332,] 0.4619897 0.7592763
##  [333,] 0.8065587 1.1364147
##  [334,] 1.3412346 0.7253645
##  [335,] 0.2803269 0.9871540
##  [336,] 0.8940759 1.8999668
##  [337,] 1.2653309 1.8489825
##  [338,] 0.9826304 0.4142808
##  [339,] 0.3679083 1.2366072
##  [340,] 0.8569586 0.5568438
##  [341,] 0.7182687 0.8474130
##  [342,] 0.3415698 0.3327361
##  [343,] 0.2978282 1.0614976
##  [344,] 1.1106885 1.5824771
##  [345,] 1.3298955 0.5865480
##  [346,] 1.1581242 1.3303097
##  [347,] 0.5407260 0.7651358
##  [348,] 0.5638898 1.3897787
##  [349,] 0.1930894 1.7343607
##  [350,] 1.0038679 1.2940914
##  [351,] 1.7103382 0.7379747
##  [352,] 0.8612485 0.9415523
##  [353,] 1.6500829 0.3309277
##  [354,] 0.2623210 0.5630772
##  [355,] 1.5784430 1.4036313
##  [356,] 0.9191741 0.8655730
##  [357,] 0.9335641 1.2952965
##  [358,] 1.1952832 0.3903943
##  [359,] 1.1757628 0.3521614
##  [360,] 0.8451408 1.5185277
##  [361,] 0.9149406 0.7112811
##  [362,] 1.1579422 1.2731178
##  [363,] 0.5203673 0.7169321
##  [364,] 1.2154667 0.6983168
##  [365,] 0.5846840 2.6407079
##  [366,] 0.5435055 1.1255652
##  [367,] 0.9317511 1.9957539
##  [368,] 0.7189463 1.0658659
##  [369,] 1.6969107 0.6935337
##  [370,] 0.7893311 1.4225102
##  [371,] 1.0120468 0.7093314
##  [372,] 0.7351945 1.2217420
##  [373,] 0.5514530 0.8071022
##  [374,] 0.7577562 0.6292271
##  [375,] 1.1194085 0.7294811
##  [376,] 1.2267407 1.6286196
##  [377,] 0.4536869 0.7818674
##  [378,] 1.4570743 0.7875590
##  [379,] 1.0377132 0.1948591
##  [380,] 0.9576295 1.2709223
##  [381,] 1.4622103 1.7069953
##  [382,] 0.6016588 1.3159509
##  [383,] 0.5008991 1.2968303
##  [384,] 0.4595523 1.5395775
##  [385,] 1.4740985 1.5860747
##  [386,] 0.9230970 0.6665131
##  [387,] 1.0215252 0.6123867
##  [388,] 0.4576422 0.3793016
##  [389,] 0.9406076 0.3440760
##  [390,] 1.1503731 0.5043904
##  [391,] 0.4444161 0.4990613
##  [392,] 0.9505087 0.9529179
##  [393,] 0.8831724 0.7235222
##  [394,] 0.7591864 0.1053986
##  [395,] 0.2115729 1.0561034
##  [396,] 0.9878755 1.2972995
##  [397,] 1.0203688 0.9872897
##  [398,] 1.1292333 1.5168421
##  [399,] 0.6583888 0.3014373
##  [400,] 1.0716096 1.0276268
##  [401,] 0.2806015 1.2879877
##  [402,] 1.5489049 0.7911830
##  [403,] 1.4271179 0.4555857
##  [404,] 0.5012535 1.2360492
##  [405,] 0.8439398 0.6750240
##  [406,] 1.4090971 0.6962206
##  [407,] 1.0478878 0.5709560
##  [408,] 0.5239471 0.3467558
##  [409,] 0.9903429 0.8977025
##  [410,] 0.8181054 0.4481577
##  [411,] 0.9135438 1.9060127
##  [412,] 0.4658236 0.8187291
##  [413,] 0.3391883 1.7436792
##  [414,] 0.7883607 1.2702968
##  [415,] 0.3013493 0.5436016
##  [416,] 1.8456421 2.1106483
##  [417,] 0.1001600 0.3979276
##  [418,] 0.5276986 0.7542158
##  [419,] 1.3188646 0.7713469
##  [420,] 0.8289761 1.2861097
##  [421,] 3.5073374 1.0052435
##  [422,] 0.8197678 1.8408260
##  [423,] 0.8727088 1.3906705
##  [424,] 0.6683358 1.0995193
##  [425,] 1.5926984 0.3641107
##  [426,] 1.0072279 0.4436548
##  [427,] 0.8468439 1.3655847
##  [428,] 1.6987003 0.6059740
##  [429,] 1.5873111 0.9168224
##  [430,] 0.8679963 1.7717739
##  [431,] 1.4245033 1.5507524
##  [432,] 0.4278994 0.9551965
##  [433,] 1.9857058 0.7368879
##  [434,] 0.5878660 1.1910514
##  [435,] 1.3170583 1.7735688
##  [436,] 1.5708102 2.4188088
##  [437,] 1.1664219 0.4552557
##  [438,] 1.4949169 1.1323808
##  [439,] 0.7735772 1.5803317
##  [440,] 0.8016199 0.6340743
##  [441,] 0.9934076 0.5371137
##  [442,] 0.8090617 1.2371924
##  [443,] 0.6517324 1.6459671
##  [444,] 0.7243453 1.4654836
##  [445,] 0.2512389 0.6498740
##  [446,] 1.6136882 0.8506197
##  [447,] 0.4346801 0.6018401
##  [448,] 1.1777906 0.4409289
##  [449,] 0.8454313 1.0027038
##  [450,] 0.6591009 1.9007943
##  [451,] 0.8517267 1.1147494
##  [452,] 1.1464940 0.6204281
##  [453,] 0.8803117 1.5322367
##  [454,] 0.7717161 0.5013128
##  [455,] 1.1861338 0.7842937
##  [456,] 2.1461894 0.1083044
##  [457,] 1.0582851 0.8551600
##  [458,] 1.7553740 2.2947750
##  [459,] 0.5888571 0.6867627
##  [460,] 1.2088618 0.5394997
##  [461,] 0.9480203 0.9963168
##  [462,] 1.5124949 1.0383481
##  [463,] 0.6411674 1.2238206
##  [464,] 3.4561227 1.1038092
##  [465,] 1.5304618 0.5663350
##  [466,] 1.0465269 0.7012104
##  [467,] 0.7643433 1.1600666
##  [468,] 1.1055518 1.2632008
##  [469,] 1.2663092 0.3981858
##  [470,] 0.6809077 0.5030872
##  [471,] 1.6473844 0.5977126
##  [472,] 1.4446657 1.1286122
##  [473,] 0.6314471 1.5530141
##  [474,] 0.6462079 1.1756275
##  [475,] 3.7965555 1.3734588
##  [476,] 0.2085922 0.7064348
##  [477,] 1.8419343 1.5048433
##  [478,] 0.5044653 1.2574069
##  [479,] 1.2787085 0.4840339
##  [480,] 0.4171365 1.2794091
##  [481,] 1.3597945 1.3084358
##  [482,] 1.8874602 0.7626490
##  [483,] 1.1874924 1.0739636
##  [484,] 0.8046895 1.5012461
##  [485,] 1.1024299 1.0433967
##  [486,] 1.6374668 0.7746183
##  [487,] 1.3138037 1.8173728
##  [488,] 1.2187472 1.1530970
##  [489,] 1.5584945 0.5126990
##  [490,] 0.6298774 0.9319731
##  [491,] 0.7018923 0.5774797
##  [492,] 0.5869563 0.6900171
##  [493,] 0.4856028 0.4501122
##  [494,] 0.5779547 0.4986825
##  [495,] 1.2637225 0.9480974
##  [496,] 1.1439418 1.6215905
##  [497,] 0.6064641 0.7338608
##  [498,] 1.1386600 1.1220225
##  [499,] 0.3494233 1.4699351
##  [500,] 0.6947993 3.1009526
##  [501,] 1.5776400 1.4880661
##  [502,] 2.2155918 0.5061614
##  [503,] 0.5733364 1.4863919
##  [504,] 0.2129977 0.8919702
##  [505,] 1.8793519 0.4886850
##  [506,] 1.2230849 1.4834148
##  [507,] 1.6416986 1.0351535
##  [508,] 1.0927031 1.0405543
##  [509,] 0.5261875 0.6561901
##  [510,] 1.6266793 0.4171891
##  [511,] 0.2803463 0.3179854
##  [512,] 0.6583914 0.6748593
##  [513,] 1.7224931 0.7327715
##  [514,] 0.7707654 0.9091183
##  [515,] 0.6741040 0.1608166
##  [516,] 1.3693976 0.4575392
##  [517,] 1.7545945 0.8883937
##  [518,] 0.5333597 1.1758476
##  [519,] 0.7255756 0.5709079
##  [520,] 1.5270277 0.8054237
##  [521,] 0.4783279 0.7830683
##  [522,] 0.3990659 0.7026919
##  [523,] 0.6896219 1.1078824
##  [524,] 1.1990523 0.8638603
##  [525,] 2.3829375 2.5094571
##  [526,] 1.2478028 0.2668300
##  [527,] 0.9993474 0.2718873
##  [528,] 0.4955198 0.4975133
##  [529,] 1.2945455 0.7620587
##  [530,] 0.2468183 0.7521018
##  [531,] 0.7397103 0.5453732
##  [532,] 0.8421605 1.2829555
##  [533,] 0.7234116 0.6250759
##  [534,] 0.3189190 1.0354408
##  [535,] 1.4661836 0.9511489
##  [536,] 1.7398399 0.9898499
##  [537,] 1.7115598 0.7503410
##  [538,] 1.1753698 1.2411293
##  [539,] 1.2914749 0.5371564
##  [540,] 0.8767461 1.1583790
##  [541,] 0.7093190 1.3887369
##  [542,] 1.0234108 0.8817127
##  [543,] 1.5540976 1.9384881
##  [544,] 1.3033895 1.2850423
##  [545,] 1.1012845 1.9208397
##  [546,] 0.8974274 0.6136702
##  [547,] 1.4590361 0.7744467
##  [548,] 1.8563680 1.9025769
##  [549,] 0.9120816 2.1809554
##  [550,] 1.5481604 0.5567406
##  [551,] 1.4974536 0.5268759
##  [552,] 1.2027748 1.3534955
##  [553,] 1.6024225 0.5430939
##  [554,] 1.0222447 0.3250967
##  [555,] 0.6419035 1.5891308
##  [556,] 1.1742932 0.7049786
##  [557,] 1.5517983 1.0989105
##  [558,] 0.9371637 1.7720880
##  [559,] 1.0208435 1.1088139
##  [560,] 0.8987720 0.7363477
##  [561,] 1.0352750 0.9646997
##  [562,] 1.5017053 0.8384398
##  [563,] 1.0147179 0.8071674
##  [564,] 1.4169807 1.0017918
##  [565,] 1.4414383 2.7672590
##  [566,] 0.6679277 0.6746273
##  [567,] 1.0522358 1.3537278
##  [568,] 0.4946633 2.3015180
##  [569,] 0.7500815 1.3466508
##  [570,] 1.6336355 0.6360026
##  [571,] 2.3873315 1.2362462
##  [572,] 1.3125334 1.0462372
##  [573,] 0.8056908 0.7560152
##  [574,] 0.3519892 1.0844896
##  [575,] 1.0547037 1.6486482
##  [576,] 0.8783543 0.7094931
##  [577,] 0.8980058 1.0623319
##  [578,] 0.6849848 1.0033170
##  [579,] 0.7709232 0.5328357
##  [580,] 1.3637149 1.2925705
##  [581,] 2.6476222 1.2732668
##  [582,] 1.1736574 2.6476969
##  [583,] 2.5716906 2.7028932
##  [584,] 1.3680221 0.5117116
##  [585,] 0.4550022 0.8024775
##  [586,] 1.0093980 1.1467734
##  [587,] 1.3019551 1.3458567
##  [588,] 0.4287069 0.3099291
##  [589,] 0.3353718 0.8729929
##  [590,] 0.5188367 0.9926451
##  [591,] 0.4640701 0.8639761
##  [592,] 1.4691336 1.2735994
##  [593,] 0.3684011 0.6355747
##  [594,] 0.4283414 1.4065252
##  [595,] 0.4081195 1.0904616
##  [596,] 1.0916977 1.3344626
##  [597,] 0.6124825 0.5558926
##  [598,] 2.3876546 0.2115251
##  [599,] 0.4037287 1.4223189
##  [600,] 1.7427445 0.8440698
##  [601,] 1.1877066 1.0173668
##  [602,] 1.1406899 0.9092335
##  [603,] 0.8908831 0.8450975
##  [604,] 0.7138546 0.7113264
##  [605,] 0.3206744 0.8112909
##  [606,] 0.7761642 1.7286400
##  [607,] 1.2429901 1.8455257
##  [608,] 0.5525702 0.2216504
##  [609,] 1.1307339 0.5608205
##  [610,] 1.9894050 1.3561352
##  [611,] 1.0689226 2.2963429
##  [612,] 1.4245158 0.2683146
##  [613,] 0.7046685 1.0008721
##  [614,] 0.3490879 0.2016493
##  [615,] 0.8548770 0.9630196
##  [616,] 2.2015631 1.0422864
##  [617,] 1.0207046 1.4785700
##  [618,] 0.4349611 0.5488037
##  [619,] 1.6251804 0.4427960
##  [620,] 1.1621590 0.2233975
##  [621,] 0.6575064 1.1787891
##  [622,] 0.8683092 0.6954316
##  [623,] 0.5060612 1.1895478
##  [624,] 1.3871841 1.4474721
##  [625,] 1.6443284 1.7731550
##  [626,] 1.1626602 0.8710047
##  [627,] 0.6997379 0.6926314
##  [628,] 1.0472968 1.1829558
##  [629,] 1.6092174 1.0632578
##  [630,] 0.7918956 0.8379512
##  [631,] 1.9378993 2.1479878
##  [632,] 1.3902109 0.7749121
##  [633,] 0.2484640 0.9998171
##  [634,] 0.9088462 0.4783105
##  [635,] 0.4302442 0.6095849
##  [636,] 0.7050889 0.6788641
##  [637,] 1.8432992 0.4664227
##  [638,] 2.2842976 0.9800107
##  [639,] 1.1578629 0.9490242
##  [640,] 2.1690041 1.9795789
##  [641,] 0.6871941 1.2396879
##  [642,] 1.0721558 0.6985972
##  [643,] 1.5735304 2.4966530
##  [644,] 0.4907352 0.9853876
##  [645,] 3.0122291 0.8797911
##  [646,] 1.1664208 1.2104788
##  [647,] 1.4513811 0.9805972
##  [648,] 0.9099203 1.2326931
##  [649,] 1.3215001 0.9943143
##  [650,] 0.9680612 1.1574810
##  [651,] 2.2103152 1.2607828
##  [652,] 0.9120537 0.2371521
##  [653,] 1.2212040 2.0924884
##  [654,] 0.9852667 1.5421202
##  [655,] 0.5839142 0.7276088
##  [656,] 0.3574030 0.7081334
##  [657,] 1.7520233 1.2315923
##  [658,] 0.9545738 1.0398862
##  [659,] 2.2170948 2.0466334
##  [660,] 1.1859514 1.7691183
##  [661,] 2.0956047 0.8494572
##  [662,] 1.3213957 0.6789020
##  [663,] 0.8612602 1.5719759
##  [664,] 0.5735758 0.8301633
##  [665,] 1.2180408 0.4055460
##  [666,] 1.4371334 0.7777779
##  [667,] 0.5814687 0.6539361
##  [668,] 0.9238557 1.6578633
##  [669,] 0.5461108 1.7261530
##  [670,] 1.4496054 0.8374622
##  [671,] 0.8112736 0.9388064
##  [672,] 0.5179548 0.9242479
##  [673,] 0.6179157 1.4809193
##  [674,] 1.0928727 1.7078406
##  [675,] 0.8603076 0.4665013
##  [676,] 0.8174957 0.5798586
##  [677,] 0.8901834 2.3718080
##  [678,] 0.8434360 0.5147555
##  [679,] 1.0165231 1.2708316
##  [680,] 0.6412628 0.8109772
##  [681,] 0.9628359 1.9724261
##  [682,] 0.8670111 1.6454024
##  [683,] 1.5338059 0.9964522
##  [684,] 2.9887641 2.7427659
##  [685,] 0.7956538 0.7227134
##  [686,] 0.7892485 0.7129698
##  [687,] 1.3580228 0.3872722
##  [688,] 0.4558355 0.2064994
##  [689,] 0.3427388 0.6539610
##  [690,] 1.2523257 0.3179014
##  [691,] 1.6368459 0.5922142
##  [692,] 0.9199678 1.3040585
##  [693,] 1.9356236 0.4282529
##  [694,] 0.6056766 0.2658254
##  [695,] 1.2626442 0.8848786
##  [696,] 0.7682327 0.5175373
##  [697,] 0.5825086 0.8098549
##  [698,] 1.5933354 0.7877992
##  [699,] 0.2719387 0.6760623
##  [700,] 0.4128934 1.2284595
##  [701,] 1.1414389 0.5265969
##  [702,] 0.7433817 0.9231503
##  [703,] 1.0971801 0.6835050
##  [704,] 0.4767049 0.5936488
##  [705,] 0.7569361 0.8945945
##  [706,] 0.4282155 1.1404023
##  [707,] 1.1455097 0.5262836
##  [708,] 0.5582155 1.4052397
##  [709,] 0.6680880 1.0939124
##  [710,] 0.8419851 1.0648067
##  [711,] 0.8756049 0.6588284
##  [712,] 1.4855438 0.7858286
##  [713,] 0.7952430 0.6860099
##  [714,] 0.5025330 0.6946269
##  [715,] 1.2321457 0.4262903
##  [716,] 0.2619687 1.5484430
##  [717,] 1.2201731 1.0484016
##  [718,] 2.1205141 0.8132115
##  [719,] 0.8514425 0.4393004
##  [720,] 1.3000004 1.0212809
##  [721,] 0.1225122 0.3543487
##  [722,] 0.9681674 1.3429191
##  [723,] 0.2463508 0.9524104
##  [724,] 0.8208026 0.3447471
##  [725,] 0.9683591 0.8327358
##  [726,] 0.6633877 1.0330029
##  [727,] 0.5692377 0.1299180
##  [728,] 0.3754544 0.6661033
##  [729,] 2.3392762 0.2893635
##  [730,] 1.8306658 1.5224859
##  [731,] 1.1100527 2.6259266
##  [732,] 0.1557883 1.0154624
##  [733,] 3.7232258 0.5923218
##  [734,] 3.0063114 0.9045910
##  [735,] 1.0610028 1.2432407
##  [736,] 0.3983563 0.8284331
##  [737,] 0.8586571 0.2284890
##  [738,] 0.9638408 0.9854984
##  [739,] 1.3245368 0.5772708
##  [740,] 2.3741223 0.9075456
##  [741,] 0.3098802 0.5827357
##  [742,] 0.3078606 0.8773913
##  [743,] 1.0113884 1.4884377
##  [744,] 1.1828203 1.7302464
##  [745,] 1.4581638 1.1030047
##  [746,] 0.8684319 1.1516594
##  [747,] 1.0032254 0.6669102
##  [748,] 0.9772989 1.1749810
##  [749,] 0.6738043 0.4676554
##  [750,] 0.1787842 0.5501696
##  [751,] 1.0044021 0.4933203
##  [752,] 0.6656481 0.6216719
##  [753,] 0.4623568 1.1749961
##  [754,] 0.8352325 0.7693856
##  [755,] 0.4201885 1.4117215
##  [756,] 1.0449122 0.7835850
##  [757,] 0.6253478 0.9113521
##  [758,] 0.8110692 1.9625250
##  [759,] 0.2881151 0.9992459
##  [760,] 0.7227180 0.8364296
##  [761,] 0.2515428 1.5086606
##  [762,] 0.8005548 1.0997582
##  [763,] 0.2021728 0.9759520
##  [764,] 0.8803604 0.7169446
##  [765,] 0.6033294 1.0744713
##  [766,] 0.5695719 0.5380103
##  [767,] 2.1844210 1.2882888
##  [768,] 1.3109725 0.8343514
##  [769,] 0.7734289 1.1705051
##  [770,] 1.2772370 1.7982242
##  [771,] 0.8510570 1.4341436
##  [772,] 0.2730946 1.4520035
##  [773,] 0.5088346 2.1815348
##  [774,] 0.8962447 1.0425626
##  [775,] 1.1506337 0.8851086
##  [776,] 1.0556097 0.7612639
##  [777,] 1.3099935 1.9880015
##  [778,] 0.6541766 1.3677700
##  [779,] 1.0367594 0.7206970
##  [780,] 1.1401624 0.5296758
##  [781,] 1.3727543 2.6433162
##  [782,] 0.7209186 1.2824811
##  [783,] 1.2370039 0.5652595
##  [784,] 1.3016810 1.0655017
##  [785,] 1.0651528 0.9900332
##  [786,] 0.9192623 1.0846283
##  [787,] 2.7316337 0.8888452
##  [788,] 1.2356377 0.6072537
##  [789,] 0.8429879 1.7774124
##  [790,] 0.6792695 0.7237951
##  [791,] 0.5137883 1.0117059
##  [792,] 0.6975670 0.5835361
##  [793,] 0.6959790 0.3623321
##  [794,] 0.9974067 0.7849763
##  [795,] 1.0444049 0.9014131
##  [796,] 0.3951821 1.6046673
##  [797,] 0.4800807 0.7236967
##  [798,] 0.6743464 1.7826001
##  [799,] 1.6446054 0.4519389
##  [800,] 1.5838862 1.2844503
##  [801,] 1.7409729 0.5148704
##  [802,] 0.4461590 0.6117800
##  [803,] 0.6893886 0.4595770
##  [804,] 1.2506738 1.9013684
##  [805,] 2.0517455 2.0358691
##  [806,] 0.6228277 0.4565032
##  [807,] 0.9259661 1.2399171
##  [808,] 1.9627551 1.2840617
##  [809,] 0.6537201 1.0257056
##  [810,] 0.6513838 0.6273337
##  [811,] 0.7915049 0.3057482
##  [812,] 0.3961761 1.2712514
##  [813,] 0.6472418 1.5030755
##  [814,] 2.2888326 1.2461410
##  [815,] 0.4725135 1.4036298
##  [816,] 0.5357719 0.5807133
##  [817,] 1.5824029 2.2088563
##  [818,] 0.6255094 1.5868429
##  [819,] 0.7765597 1.0682722
##  [820,] 0.5841069 0.8499209
##  [821,] 0.3585005 1.0925057
##  [822,] 1.1378691 0.4505460
##  [823,] 1.6453440 0.5690062
##  [824,] 0.3341070 1.7304638
##  [825,] 0.2129236 0.8903641
##  [826,] 0.7305571 0.8944324
##  [827,] 0.2592391 1.8510019
##  [828,] 0.7313600 1.3096716
##  [829,] 1.2225318 0.6868632
##  [830,] 1.0805237 1.2376928
##  [831,] 0.6861552 0.7704690
##  [832,] 1.0310521 1.1217127
##  [833,] 0.7229002 0.6008686
##  [834,] 0.8594878 0.5090439
##  [835,] 0.6456431 0.5389815
##  [836,] 1.0497801 0.9056697
##  [837,] 0.7743263 0.5823938
##  [838,] 0.2775914 0.6600846
##  [839,] 1.0734097 1.0981067
##  [840,] 1.3724453 0.6762862
##  [841,] 0.6200563 1.4369126
##  [842,] 0.4221652 0.7497118
##  [843,] 0.1887104 0.4511190
##  [844,] 0.8905813 1.0713214
##  [845,] 0.4492508 0.9611427
##  [846,] 1.2266377 0.9239308
##  [847,] 1.8357903 0.6139745
##  [848,] 2.1170610 1.5297623
##  [849,] 0.8641904 0.9048875
##  [850,] 0.7763564 0.8261014
##  [851,] 0.5886437 0.9219957
##  [852,] 0.7780805 1.2198779
##  [853,] 0.3130145 1.0273264
##  [854,] 1.3037881 1.7243142
##  [855,] 0.6600778 0.1135421
##  [856,] 0.3405642 1.2357915
##  [857,] 1.6048183 1.0667869
##  [858,] 0.7850148 0.9659300
##  [859,] 1.4330423 0.7837892
##  [860,] 1.9417944 1.5471746
##  [861,] 0.7368109 0.9799005
##  [862,] 0.4443651 1.4897043
##  [863,] 0.8096961 1.5027805
##  [864,] 0.3342372 0.5853036
##  [865,] 0.6936222 1.0112454
##  [866,] 0.7970887 1.7889110
##  [867,] 0.9834582 0.7641085
##  [868,] 0.7640428 0.5700905
##  [869,] 1.6414408 0.5670252
##  [870,] 0.9302196 1.7945324
##  [871,] 0.8533056 0.4033542
##  [872,] 0.2482495 1.1677066
##  [873,] 0.7998040 0.8428989
##  [874,] 0.8520182 0.3752923
##  [875,] 0.6009293 1.3048680
##  [876,] 0.3443136 0.9950623
##  [877,] 2.2497036 0.6300975
##  [878,] 0.7127964 1.6250996
##  [879,] 0.9553326 1.3863370
##  [880,] 0.3400701 1.0058723
##  [881,] 0.8357676 0.4586675
##  [882,] 0.6962055 0.2049235
##  [883,] 1.0528344 0.9543984
##  [884,] 0.6551738 1.5340469
##  [885,] 1.9641078 1.6183076
##  [886,] 1.0440074 0.5125522
##  [887,] 0.8646239 0.5517355
##  [888,] 0.6761364 2.8340474
##  [889,] 0.7399453 1.2953866
##  [890,] 1.4787130 1.0693455
##  [891,] 1.1775275 2.5238715
##  [892,] 2.1987639 0.7572682
##  [893,] 1.7449447 1.4987778
##  [894,] 0.2214034 1.1560529
##  [895,] 1.9745993 0.4945942
##  [896,] 1.5273327 0.4593395
##  [897,] 1.1017223 0.4914373
##  [898,] 0.6719017 1.1670288
##  [899,] 0.3934572 0.5766324
##  [900,] 0.3379552 2.1638225
##  [901,] 0.4180118 1.4133276
##  [902,] 0.5052528 0.2869777
##  [903,] 1.1425264 0.5547063
##  [904,] 4.2820413 1.1374841
##  [905,] 0.6944172 0.5522295
##  [906,] 1.0518811 0.9191484
##  [907,] 1.1865574 0.9241486
##  [908,] 1.4206617 0.3614167
##  [909,] 0.5846067 0.6777883
##  [910,] 0.8763929 1.5577614
##  [911,] 0.7876491 1.1484446
##  [912,] 0.5163299 0.3901655
##  [913,] 0.8104888 2.4508215
##  [914,] 0.7794721 0.5401396
##  [915,] 1.2704495 0.3891202
##  [916,] 1.9685345 1.7703449
##  [917,] 0.7167361 0.4780141
##  [918,] 1.0570261 0.9129683
##  [919,] 0.5217457 1.0365086
##  [920,] 1.6125546 1.2231105
##  [921,] 0.7641024 0.6249500
##  [922,] 0.5860518 0.9734472
##  [923,] 0.9238994 1.2624703
##  [924,] 1.8888542 1.5093125
##  [925,] 2.3520741 0.5955637
##  [926,] 1.1756421 2.0979918
##  [927,] 2.3694816 1.2120009
##  [928,] 1.2284399 0.2796685
##  [929,] 0.6708727 0.7965035
##  [930,] 1.3412596 0.5425654
##  [931,] 0.6410777 1.1444281
##  [932,] 0.9475407 0.3676355
##  [933,] 2.0426579 1.8595329
##  [934,] 1.7386576 0.5958084
##  [935,] 1.1496454 0.2358684
##  [936,] 1.7468585 1.9488821
##  [937,] 1.9264065 1.3434620
##  [938,] 0.7164047 0.6779951
##  [939,] 1.2738789 0.4462101
##  [940,] 1.7310872 2.1168610
##  [941,] 1.3538728 1.5235136
##  [942,] 1.5599813 0.9691400
##  [943,] 1.3243285 0.9422121
##  [944,] 0.8639356 0.3694354
##  [945,] 0.7146255 0.6606062
##  [946,] 1.0115684 0.7496037
##  [947,] 0.9213956 0.4255782
##  [948,] 1.1378723 0.8560517
##  [949,] 1.3275265 2.1810385
##  [950,] 1.1477997 1.0120646
##  [951,] 0.6967618 0.6100558
##  [952,] 0.5578072 0.6216000
##  [953,] 0.7405553 0.3102498
##  [954,] 0.5705637 0.5106031
##  [955,] 0.5142820 0.7053741
##  [956,] 0.7047356 0.4248170
##  [957,] 1.1754134 1.2774289
##  [958,] 0.3332258 0.7335940
##  [959,] 0.7120403 1.2160229
##  [960,] 1.5087946 0.2823302
##  [961,] 0.4903416 1.0958285
##  [962,] 0.5004908 1.0891064
##  [963,] 0.9389418 0.4255239
##  [964,] 0.6168014 0.7755318
##  [965,] 1.3034819 2.3649265
##  [966,] 0.4487397 1.1360021
##  [967,] 1.2674244 1.0664486
##  [968,] 1.5720549 0.6919854
##  [969,] 1.4310354 0.4513660
##  [970,] 1.2368114 0.8792416
##  [971,] 0.4804327 2.2200502
##  [972,] 0.4186984 1.2531901
##  [973,] 0.1218204 1.6404477
##  [974,] 0.4654093 0.8988662
##  [975,] 1.0986846 0.8368617
##  [976,] 0.5698935 0.9670671
##  [977,] 0.7725930 0.5185224
##  [978,] 0.4062727 0.8478946
##  [979,] 1.2007296 0.8209012
##  [980,] 0.6305821 1.3164336
##  [981,] 1.7051376 1.6385660
##  [982,] 0.9498648 2.5324336
##  [983,] 1.1589795 0.3622011
##  [984,] 1.0845641 1.6226098
##  [985,] 3.7830547 0.3845841
##  [986,] 0.8440801 1.3649315
##  [987,] 1.0566599 1.1398269
##  [988,] 0.3845612 0.9261189
##  [989,] 1.4414629 0.6286629
##  [990,] 0.4720613 1.1402347
##  [991,] 1.1868236 0.9437842
##  [992,] 1.5059606 0.8569690
##  [993,] 1.1354860 0.8517288
##  [994,] 0.9749544 0.8880004
##  [995,] 0.4320570 1.4335156
##  [996,] 0.9551517 0.3304445
##  [997,] 0.9104851 0.7420362
##  [998,] 0.6270105 0.4702040
##  [999,] 1.1531363 1.4686492
## 
## $model.matrix
##    (Intercept) microsite1 shrub_density
## 1            1          1            11
## 2            1          1            12
## 3            1         -1             0
## 4            1         -1             0
## 5            1          1            11
## 6            1          1            10
## 7            1         -1             0
## 8            1         -1             0
## 9            1          1            14
## 10           1          1            13
## 11           1         -1             0
## 12           1         -1             0
## 13           1          1            11
## 14           1          1            11
## 15           1         -1             0
## 16           1          1            10
## 17           1          1            11
## 18           1          1            11
## 19           1          1            10
## 20           1         -1             0
## 21           1         -1             0
## 22           1         -1             0
## 23           1         -1             0
## 
## $terms
## pca_data_2023 ~ microsite * shrub_density
## attr(,"variables")
## list(pca_data_2023, microsite, shrub_density)
## attr(,"factors")
##               microsite shrub_density microsite:shrub_density
## pca_data_2023         0             0                       0
## microsite             1             0                       1
## shrub_density         0             1                       1
## attr(,"term.labels")
## [1] "microsite"               "shrub_density"          
## [3] "microsite:shrub_density"
## attr(,"order")
## [1] 1 1 2
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## attr(,"class")
## [1] "adonis"
dist_2023 <- vegdist(pca_data_2023, species = "bray")
res_2023 <- pcoa(dist_2023)
p2 <- as.data.frame(res_2023$vectors)%>%
  dplyr::select(Axis.1, Axis.2) %>%
  bind_cols(env_2023,.)

ggplot(p2, aes(Axis.1, Axis.2, group = microsite)) +
  geom_point(aes(color = microsite)) +
  geom_text(aes(label=plot), hjust = 0, vjust = 0, check_overlap = TRUE, nudge_x = 0.01)+
  scale_color_brewer(palette = "Set1") +
  labs(color = "", subtitle = "labels denote plot identity")

model02 <- betadisper(dist_2023, env_2023$microsite)
model02
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_2023, group = env_2023$microsite)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 7
## 
## Average distance to median:
## Density    Open 
##  0.4638  0.5348 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 22 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.0914 1.4576 1.0790 0.5277 0.4666 0.3903 0.3612 0.1835
anova(model02)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq F value Pr(>F)
## Groups     1 0.02894 0.028937  1.5275 0.2301
## Residuals 21 0.39782 0.018944
permutest(model02,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq      F N.Perm Pr(>F)
## Groups     1 0.02894 0.028937 1.5275     99   0.22
## Residuals 21 0.39782 0.018944                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##         Density Open
## Density         0.26
## Open    0.23013
model02.HSD <- TukeyHSD(model02)
boxplot(model02)

model03 <- betadisper(dist_2023, env_2023$shrub_density)
model03
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_2023, group = env_2023$shrub_density)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 7
## 
## Average distance to median:
##      0     10     11     12     13     14 
## 0.5348 0.3051 0.4393 0.0000 0.0000 0.0000 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 22 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.0914 1.4576 1.0790 0.5277 0.4666 0.3903 0.3612 0.1835
anova(model03)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq F value   Pr(>F)   
## Groups     5 0.71375 0.142751    4.86 0.006083 **
## Residuals 17 0.49934 0.029373                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(model03,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq    F N.Perm Pr(>F)  
## Groups     5 0.71375 0.142751 4.86     99   0.02 *
## Residuals 17 0.49934 0.029373                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##           0       10       11 12 13 14
## 0           0.030000 0.150000         
## 10 0.059818          0.380000         
## 11 0.192393 0.435177                  
## 12                                    
## 13                                    
## 14
model03.HSD <- TukeyHSD(model03)
boxplot(model03)

model04 <- betadisper(dist_2023, env_2023$site)
model04
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_2023, group = env_2023$site)
## 
## No. of Positive Eigenvalues: 15
## No. of Negative Eigenvalues: 7
## 
## Average distance to median:
## Carrizo  Cuyama  Tecopa 
##  0.5093  0.4594  0.4488 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 22 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.0914 1.4576 1.0790 0.5277 0.4666 0.3903 0.3612 0.1835
anova(model04)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq   Mean Sq F value Pr(>F)
## Groups     2 0.01656 0.0082795  0.4577 0.6392
## Residuals 20 0.36181 0.0180906
permutest(model04,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq   Mean Sq      F N.Perm Pr(>F)
## Groups     2 0.01656 0.0082795 0.4577     99   0.71
## Residuals 20 0.36181 0.0180906                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##         Carrizo  Cuyama Tecopa
## Carrizo         0.66000   0.14
## Cuyama  0.56406           0.92
## Tecopa  0.14036 0.89377
model04.HSD <- TukeyHSD(model04)
boxplot(model04)

### From running the community compositions both in 2022 and 2023 it seems the community compositions across densities, microsites, and sites are all somewhat similar with no significant differences.

Run PCOAs for both years combined!

photo_final <- read.csv("observations_final.csv")
summary(photo_final)
##     region              site            site_code          microsite        
##  Length:250716      Length:250716      Length:250716      Length:250716     
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##       plot           cam_ID         month               date          
##  Min.   :1.000   Min.   :1.000   Length:250716      Length:250716     
##  1st Qu.:1.000   1st Qu.:1.000   Class :character   Class :character  
##  Median :2.000   Median :1.000   Mode  :character   Mode  :character  
##  Mean   :1.772   Mean   :1.498                                        
##  3rd Qu.:2.000   3rd Qu.:2.000                                        
##  Max.   :4.000   Max.   :2.000                                        
##       year      shrub_density         rep         identified_by     
##  Min.   :2022   Min.   : 0.000   Min.   :     1   Length:250716     
##  1st Qu.:2023   1st Qu.: 0.000   1st Qu.: 21744   Class :character  
##  Median :2023   Median :10.000   Median : 67344   Mode  :character  
##  Mean   :2023   Mean   : 5.878   Mean   : 77566                     
##  3rd Qu.:2023   3rd Qu.:11.000   3rd Qu.:130022                     
##  Max.   :2023   Max.   :14.000   Max.   :192701                     
##    filename          timestamp           animal.hit         class          
##  Length:250716      Length:250716      Min.   :0.00000   Length:250716     
##  Class :character   Class :character   1st Qu.:0.00000   Class :character  
##  Mode  :character   Mode  :character   Median :0.00000   Mode  :character  
##                                        Mean   :0.01923                     
##                                        3rd Qu.:0.00000                     
##                                        Max.   :1.00000                     
##     order              family             genus             species         
##  Length:250716      Length:250716      Length:250716      Length:250716     
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  common_name        number_of_objects
##  Length:250716      Min.   : 1       
##  Class :character   1st Qu.: 1       
##  Mode  :character   Median : 1       
##                     Mean   : 1       
##                     3rd Qu.: 1       
##                     Max.   :12
photo_final <- photo_final %>%
  filter(common_name != "Human")
photo_final <- photo_final %>%
  filter(common_name != "Human-Camera Trapper")
photo_final <- photo_final %>%
  filter(common_name != "Domestic Dog")
photo_final <- photo_final %>%
  filter(common_name != "Vehicle")
photo_final <- photo_final %>%
  dplyr::filter(common_name != "Insect")
photo_final <- photo_final %>%
  dplyr::filter(common_name != "Animal")
photo_final <- photo_final %>%
  dplyr::filter(common_name != "Bird")
  
count.hit_final <- photo_final %>%
  count(animal.hit) %>%
  na.omit()
summary(count.hit_final)
##    animal.hit         n         
##  Min.   :0.00   Min.   :  3717  
##  1st Qu.:0.25   1st Qu.: 64261  
##  Median :0.50   Median :124806  
##  Mean   :0.50   Mean   :124806  
##  3rd Qu.:0.75   3rd Qu.:185350  
##  Max.   :1.00   Max.   :245894
# Wow we have a 1.489% capture rate for the project!
### Animal Observations by Site_Code
animals_by_sitecode_final <- photo_final%>%
  group_by(site_code, microsite, common_name) %>%
  summarise(captures = sum(animal.hit), n = n())
## `summarise()` has grouped output by 'site_code', 'microsite'. You can override
## using the `.groups` argument.
animals_by_sitecode_final <- animals_by_sitecode_final %>%
  filter(common_name != "Blank") %>% filter(common_name != "No CV Result") 
animals_by_site_final <- photo_final %>% group_by(site,microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site', 'microsite'. You can override using
## the `.groups` argument.
animals_by_site_final <- animals_by_site_final %>% filter(common_name != "Blank") %>% filter(common_name != "No CV Result")
animals_by_density_final<- photo_final %>% group_by(microsite,common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'microsite'. You can override using the
## `.groups` argument.
animals_by_density_final <- animals_by_density_final %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result")
Total_Observations_final <- photo_final %>% group_by(common_name) %>% summarise(total = sum(animal.hit)) %>% filter(common_name != "Blank")  %>% filter(common_name != "No CV Result") %>% filter(common_name != "Mammal")
density_obvs_final <- merge(animals_by_density_final, Total_Observations_final, all = TRUE) %>% filter(common_name != "Mammal")
density_obvs_final$percent_presence <- density_obvs_final$captures/density_obvs_final$total
m3<- glm(total ~ microsite*common_name, family = "poisson", data = density_obvs_final)
anova(m3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: total
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     55      27821              
## microsite              1     29.6        54      27791 5.449e-08 ***
## common_name           32  27791.1        22          0 < 2.2e-16 ***
## microsite:common_name 22      0.0         0          0         1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e3 <- emmeans(m3, pairwise~common_name)
## NOTE: Results may be misleading due to involvement in interactions
#head(e3)
animals_density_final <- photo_final %>% group_by(site_code,microsite,plot, shrub_density, common_name) %>% summarise(captures = sum(animal.hit))
## `summarise()` has grouped output by 'site_code', 'microsite', 'plot',
## 'shrub_density'. You can override using the `.groups` argument.
animals_density_final <- animals_density_final %>% filter(common_name != "Blank") %>% filter(common_name != "Mammal")
pca_data_final <- animals_density_final ### Created new df for pca data
pca_data_final <- pca_data_final %>%
  spread(common_name, captures) %>%
  ungroup() %>%
  dplyr::select(-site_code, -microsite, -plot) %>%
  replace(is.na(.),0)
dim(pca_data_final)
## [1] 24 35
env_final <- read.csv("environment_final.csv") ### Drop Tecopa open 1, Tecopa open 4, since they have no animal observations.
dim(env_final)
## [1] 24  5
model010 <- adonis(pca_data_final ~ microsite*shrub_density, data = env_final)
## 'adonis' will be deprecated: use 'adonis2' instead
model010
## $aov.tab
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##               Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## microsite      1    0.2680 0.26799  1.0165 0.04244  0.350  
## shrub_density  1    0.5102 0.51024  1.9354 0.08081  0.093 .
## Residuals     21    5.5363 0.26363         0.87675         
## Total         23    6.3145                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $call
## adonis(formula = pca_data_final ~ microsite * shrub_density, 
##     data = env_final)
## 
## $coefficients
##                          shrub_density American Robin Black-tailed Jackrabbit
## (Intercept)                 -10.557692   4.166667e-02              -11.346154
## microsite1                  -14.057692  -4.166667e-02              -22.012821
## shrub_density                 2.876923   9.476236e-19                4.661538
## microsite1:shrub_density            NA             NA                      NA
##                          Black-throated Sparrow Blunt-nosed Leopard Lizard
## (Intercept)                        4.166667e-02                  1.1185897
## microsite1                        -4.166667e-02                  1.0352564
## shrub_density                      4.564605e-18                 -0.1692308
## microsite1:shrub_density                     NA                         NA
##                              Bobcat Brewer's Blackbird
## (Intercept)              -0.7019231         -2.4070513
## microsite1               -1.1185897         -2.8237179
## shrub_density             0.1692308          0.5538462
## microsite1:shrub_density         NA                 NA
##                          California Ground Squirrel California Pocket Mouse
## (Intercept)                               19.618590              0.33974359
## microsite1                                13.868590              0.17307692
## shrub_density                             -1.769231             -0.03076923
## microsite1:shrub_density                         NA                      NA
##                          California Quail California Thrasher Common Raven
## (Intercept)                     -6.185897                -1.0    2.5961538
## microsite1                      -7.352564                -1.0   -1.9038462
## shrub_density                    1.292308                 0.2    0.1384615
## microsite1:shrub_density               NA                  NA           NA
##                              Coyote Desert Cottontail Desert Iguana
## (Intercept)               3.2467949        -27.230769  1.958333e+00
## microsite1               -2.8365385        -28.897436 -1.958333e+00
## shrub_density             0.4153846          5.307692  3.783904e-16
## microsite1:shrub_density         NA                NA            NA
##                          Giant Kangaroo Rat Great White Egret
## (Intercept)                       6.8141026      4.166667e-02
## microsite1                        4.6474359     -4.166667e-02
## shrub_density                    -0.7076923      4.564605e-18
## microsite1:shrub_density                 NA                NA
##                          Greater Roadrunner Heermann's Kangaroo Rat Horned Lark
## (Intercept)                      -4.3814103              125.403846  0.38461538
## microsite1                       -4.4647436               50.903846  0.38461538
## shrub_density                     0.8307692               -4.538462 -0.04615385
## microsite1:shrub_density                 NA                      NA          NA
##                               Killdeer    Kit Fox Lark Sparrow
## (Intercept)               4.166667e-02  2.5288462   -1.8717949
## microsite1               -4.166667e-02  2.1121795   -2.2051282
## shrub_density             4.564605e-18 -0.3384615    0.3846154
## microsite1:shrub_density            NA         NA           NA
##                          Loggerhead Shrike Merriam's Kangaroo Rat
## (Intercept)                     -1.1025641             1.06089744
## microsite1                      -1.4358974             0.14423077
## shrub_density                    0.2923077            -0.09230769
## microsite1:shrub_density                NA                     NA
##                          Mohave Ground Squirrel Mourning Dove
## (Intercept)                        2.916667e-01    -1.9551282
## microsite1                        -2.916667e-01    -2.1217949
## shrub_density                     -1.570024e-16     0.3846154
## microsite1:shrub_density                     NA            NA
##                          Nelson's Antelope Squirrel No CV Result
## (Intercept)                               18.894231   -0.8685897
## microsite1                                13.977564   -0.9519231
## shrub_density                             -2.092308    0.1692308
## microsite1:shrub_density                         NA           NA
##                          Red-tailed Hawk Salinas Pocket Mouse Say's Phoebe
## (Intercept)                   -0.5641026          -0.35256410  0.253205128
## microsite1                    -0.5641026          -0.51923077  0.003205128
## shrub_density                  0.1076923           0.09230769 -0.015384615
## microsite1:shrub_density              NA                   NA           NA
##                          Vesper Sparrow Western whiptail
## (Intercept)                   1.5801282       0.12820513
## microsite1                    1.4967949       0.12820513
## shrub_density                -0.1846154      -0.01538462
## microsite1:shrub_density             NA               NA
##                          White-tailed Antelope Squirrel
## (Intercept)                                  0.33653846
## microsite1                                  -0.08012821
## shrub_density                               -0.01538462
## microsite1:shrub_density                             NA
## 
## $coef.sites
##                                    1           2           3           4
## (Intercept)               0.78080317  0.82434750  0.98306093  0.76605527
## microsite1                0.17504154  0.26134577  0.28849450  0.24337903
## shrub_density            -0.03080745 -0.04609079 -0.04138812 -0.03373393
## microsite1:shrub_density          NA          NA          NA          NA
##                                    5           6           7           8
## (Intercept)               0.84838652  0.83124969  0.86997845  0.76272593
## microsite1                0.30313950  0.28542834  0.29904628  0.20499025
## shrub_density            -0.05068255 -0.04597727 -0.04282439 -0.02976002
## microsite1:shrub_density          NA          NA          NA          NA
##                                   9         10          11         12
## (Intercept)               1.7481015  1.5203179  1.00167997  1.0125329
## microsite1                1.0946409  0.9430041  0.41975528  0.4948288
## shrub_density            -0.1923781 -0.1650103 -0.07142752 -0.0794049
## microsite1:shrub_density         NA         NA          NA         NA
##                                   13          14         15          16
## (Intercept)               0.88500919  0.84806327  0.8076157  0.83755826
## microsite1                0.18017241  0.07715532  0.2071152  0.27863228
## shrub_density            -0.03799694 -0.02089895 -0.0336203 -0.04242666
## microsite1:shrub_density          NA          NA         NA          NA
##                                   17          18          19          20
## (Intercept)               0.04881892  0.31671402  0.25149293  0.07189331
## microsite1               -0.82473427 -0.56994858 -0.63539881 -0.82608604
## shrub_density             0.13158888  0.08613734  0.09735222  0.13310018
## microsite1:shrub_density          NA          NA          NA          NA
##                                   21          22          23           24
## (Intercept)               1.12355908  1.11712532  1.06379973  0.830255162
## microsite1                0.41343026  0.46257310  0.31720419  0.079719825
## shrub_density            -0.06585209 -0.07418334 -0.04509589 -0.006831989
## microsite1:shrub_density          NA          NA          NA           NA
## 
## $f.perms
##               [,1]       [,2]
##    [1,] 0.23496499 0.76822600
##    [2,] 0.09262485 0.78962868
##    [3,] 1.18384241 1.26968747
##    [4,] 0.57125392 0.31991878
##    [5,] 0.87128256 0.12714980
##    [6,] 0.35392365 0.57198682
##    [7,] 2.17368995 1.35872842
##    [8,] 2.08285104 1.13426979
##    [9,] 1.36433165 1.13533064
##   [10,] 0.87152326 1.27718874
##   [11,] 1.80510162 1.20285210
##   [12,] 1.22711455 0.77486169
##   [13,] 0.55485593 0.60529275
##   [14,] 0.51329958 1.08130429
##   [15,] 0.81333146 0.92130702
##   [16,] 0.21106459 0.75207613
##   [17,] 0.62200224 1.75191490
##   [18,] 1.31580411 0.77065101
##   [19,] 1.30913225 1.77719594
##   [20,] 0.29381370 0.79190199
##   [21,] 0.92878270 0.82689638
##   [22,] 0.65787974 1.15645742
##   [23,] 1.35407052 1.72986031
##   [24,] 1.16148447 0.71405687
##   [25,] 0.61306997 1.25917298
##   [26,] 3.04091314 1.43482159
##   [27,] 1.19171173 0.47147925
##   [28,] 0.96115296 2.29478556
##   [29,] 0.60245941 0.82175516
##   [30,] 1.17128084 1.08757781
##   [31,] 0.40921525 0.16592538
##   [32,] 0.42484241 0.65679364
##   [33,] 1.32529812 0.84093876
##   [34,] 1.20355413 0.57478006
##   [35,] 0.47409043 1.43136717
##   [36,] 0.40839782 1.02353742
##   [37,] 1.78289211 0.62306854
##   [38,] 0.27561241 0.45059042
##   [39,] 0.61379139 0.50412058
##   [40,] 0.71339354 0.04957232
##   [41,] 0.64191262 1.14814601
##   [42,] 1.06574934 1.83195204
##   [43,] 0.47305735 1.27191887
##   [44,] 0.81681129 0.99825885
##   [45,] 1.84026590 0.60303259
##   [46,] 0.36552672 1.04491054
##   [47,] 0.34691104 1.13974393
##   [48,] 0.69445817 0.67169563
##   [49,] 0.57180786 0.60790895
##   [50,] 1.08892673 1.13312879
##   [51,] 0.39566204 1.22019889
##   [52,] 0.40118071 0.66226615
##   [53,] 0.96721055 1.01216833
##   [54,] 2.72519774 0.54672642
##   [55,] 0.90114879 1.25828231
##   [56,] 0.45828575 0.77411083
##   [57,] 0.38296044 0.99896338
##   [58,] 2.63183224 0.41259748
##   [59,] 1.10815434 1.33958340
##   [60,] 1.14829028 0.59348135
##   [61,] 3.16349145 0.30148756
##   [62,] 0.49226254 0.76437714
##   [63,] 0.47147549 0.62199387
##   [64,] 1.24956567 0.60280292
##   [65,] 2.55197016 1.34633592
##   [66,] 0.77672126 0.39741696
##   [67,] 1.05819297 0.51260812
##   [68,] 0.51481016 1.38842748
##   [69,] 0.48936077 0.82768205
##   [70,] 1.31595954 0.84850599
##   [71,] 0.54312278 0.45900817
##   [72,] 1.56946007 1.18525528
##   [73,] 1.03203900 0.95503071
##   [74,] 1.50534580 2.00793214
##   [75,] 0.78320188 1.24361365
##   [76,] 0.43910399 0.53117859
##   [77,] 0.85296329 2.55225247
##   [78,] 0.54418543 1.05499846
##   [79,] 0.30065605 0.55230929
##   [80,] 0.81400978 1.05495652
##   [81,] 1.57200386 1.20741046
##   [82,] 2.01193873 1.06802623
##   [83,] 1.23898562 1.60966910
##   [84,] 0.34608247 1.32901461
##   [85,] 0.60540667 1.68122000
##   [86,] 0.70090906 0.23643450
##   [87,] 0.37018345 1.38374964
##   [88,] 0.27402380 0.21760893
##   [89,] 0.97201067 0.76773463
##   [90,] 0.36969817 0.63978732
##   [91,] 0.44285040 0.37010608
##   [92,] 0.68820415 1.28244589
##   [93,] 1.32181129 1.47178016
##   [94,] 0.70340487 1.85184083
##   [95,] 1.22137542 1.15580348
##   [96,] 1.07909015 1.18784623
##   [97,] 2.59015383 0.43232040
##   [98,] 0.35477374 0.89806208
##   [99,] 0.54387297 0.25645687
##  [100,] 1.02867024 0.71884632
##  [101,] 0.70688312 1.21693517
##  [102,] 0.96991024 0.33943583
##  [103,] 0.67086163 0.56789582
##  [104,] 0.99954014 1.52061233
##  [105,] 2.86087470 0.51774225
##  [106,] 0.78329801 0.26357793
##  [107,] 1.95279825 1.28736227
##  [108,] 2.52627037 1.07544489
##  [109,] 0.75917183 0.96515201
##  [110,] 1.47933680 0.76925569
##  [111,] 1.07448800 0.83606625
##  [112,] 0.61778563 0.86103001
##  [113,] 1.01175732 1.05922976
##  [114,] 1.04001402 0.80499863
##  [115,] 0.36784659 2.18958840
##  [116,] 0.35349119 0.47400929
##  [117,] 0.92024277 3.02365204
##  [118,] 0.49843473 1.29407481
##  [119,] 0.16519736 1.02703752
##  [120,] 3.60215479 4.09922213
##  [121,] 0.64748969 0.84909117
##  [122,] 0.97227726 0.46225445
##  [123,] 0.85779803 1.37842307
##  [124,] 0.41284416 1.05877495
##  [125,] 1.43512238 0.90422665
##  [126,] 0.63549206 0.63588864
##  [127,] 2.25620928 1.00807733
##  [128,] 0.68819317 1.09436543
##  [129,] 0.66003448 1.26129678
##  [130,] 0.55465950 0.34856940
##  [131,] 0.67452428 1.08348688
##  [132,] 0.37027455 1.40899783
##  [133,] 0.84616144 1.76434489
##  [134,] 0.96254284 0.84543650
##  [135,] 0.94278679 0.42203839
##  [136,] 0.61415909 1.09665447
##  [137,] 0.72564851 1.02409447
##  [138,] 1.81477909 0.57145896
##  [139,] 0.30017708 1.00338418
##  [140,] 0.76325194 0.95073779
##  [141,] 1.74536118 0.19128239
##  [142,] 2.38025595 0.53772008
##  [143,] 0.58619960 0.39404703
##  [144,] 1.08766112 0.57801442
##  [145,] 1.19151084 1.68009279
##  [146,] 1.81772224 0.26932175
##  [147,] 0.57721586 0.54115892
##  [148,] 1.44656976 0.35487447
##  [149,] 0.32281866 0.34805550
##  [150,] 1.13899089 0.77161896
##  [151,] 0.90746361 0.72461985
##  [152,] 1.27903982 1.69308437
##  [153,] 0.38856981 0.19946582
##  [154,] 0.71491349 0.37221828
##  [155,] 0.83061118 0.30289671
##  [156,] 0.57332442 0.46858393
##  [157,] 2.13079914 0.77731826
##  [158,] 1.82279217 0.38564811
##  [159,] 0.81474769 1.28368930
##  [160,] 0.66715899 0.25442281
##  [161,] 1.50063894 0.69963219
##  [162,] 2.69875437 0.75400009
##  [163,] 1.94894501 3.03488354
##  [164,] 0.26210100 0.98694408
##  [165,] 0.57075177 0.60806065
##  [166,] 0.37860271 1.37008547
##  [167,] 1.11665152 1.14622578
##  [168,] 0.59338012 0.54393255
##  [169,] 0.82346503 0.74708163
##  [170,] 0.98027952 1.43347113
##  [171,] 0.67424219 1.08330196
##  [172,] 0.20376826 0.81721116
##  [173,] 0.53075044 0.48261081
##  [174,] 0.84099286 0.67146963
##  [175,] 0.77816047 1.07351881
##  [176,] 0.49296191 2.23734317
##  [177,] 1.45006564 1.16440119
##  [178,] 0.79602786 0.61307255
##  [179,] 0.44377160 0.63529680
##  [180,] 0.74583253 1.13846282
##  [181,] 1.87256788 0.89777274
##  [182,] 0.55513451 0.66704391
##  [183,] 0.79187215 0.59276757
##  [184,] 0.52393202 0.97500224
##  [185,] 1.03140071 0.56333618
##  [186,] 1.08411182 0.62303549
##  [187,] 0.47003035 0.33991961
##  [188,] 0.66233133 0.84642238
##  [189,] 1.25907307 0.92713518
##  [190,] 1.58721954 1.84937902
##  [191,] 1.65703053 0.50157984
##  [192,] 1.69792511 1.32153299
##  [193,] 1.12405265 0.75721310
##  [194,] 0.15001982 0.90113233
##  [195,] 0.95859902 1.15299575
##  [196,] 0.62385738 1.55647744
##  [197,] 2.32738051 1.18106587
##  [198,] 0.94397100 0.92355499
##  [199,] 1.42815390 0.59202929
##  [200,] 1.07149797 1.08039971
##  [201,] 0.30295843 0.22647207
##  [202,] 0.92065095 0.22075479
##  [203,] 0.60398728 0.59814691
##  [204,] 1.00086191 1.25091170
##  [205,] 0.90859917 0.42034767
##  [206,] 0.55287135 1.12024521
##  [207,] 1.04847958 0.39442770
##  [208,] 1.04345929 1.99764923
##  [209,] 3.86803730 2.13959800
##  [210,] 0.36993936 2.38978789
##  [211,] 0.17238469 0.79280446
##  [212,] 1.01591937 0.94828480
##  [213,] 1.88663580 0.65076264
##  [214,] 1.01205722 0.97782396
##  [215,] 0.95497428 0.14763276
##  [216,] 1.01802204 0.73677650
##  [217,] 0.65711066 2.46777280
##  [218,] 1.10046370 1.23546395
##  [219,] 0.51448353 2.07089544
##  [220,] 0.54101344 1.48541975
##  [221,] 1.44514787 1.50623721
##  [222,] 0.82863072 1.08739610
##  [223,] 0.79319000 1.48236777
##  [224,] 3.50382285 0.10063593
##  [225,] 1.00023433 2.01904878
##  [226,] 0.83598186 0.92834611
##  [227,] 1.81025856 1.41169606
##  [228,] 0.62484540 1.49006575
##  [229,] 0.30484097 1.14592517
##  [230,] 0.90203826 0.66393283
##  [231,] 0.51609709 0.59620228
##  [232,] 1.56121546 2.01887089
##  [233,] 2.47703657 3.54717428
##  [234,] 0.82901295 0.93159165
##  [235,] 1.02293334 0.23793669
##  [236,] 0.35125761 1.30311031
##  [237,] 0.69746460 0.84413677
##  [238,] 1.70146701 1.68056892
##  [239,] 0.55414092 0.44755628
##  [240,] 0.62833012 1.45677859
##  [241,] 0.37729532 0.77959687
##  [242,] 0.60634140 0.32452251
##  [243,] 0.62777299 0.24791233
##  [244,] 2.11441142 0.76470928
##  [245,] 1.90639377 1.39181232
##  [246,] 0.48480877 0.40252303
##  [247,] 0.32313667 0.34969310
##  [248,] 0.20460734 0.40942160
##  [249,] 2.43049778 0.46401759
##  [250,] 0.63676153 0.58590490
##  [251,] 0.34780438 1.06581693
##  [252,] 0.47887521 2.68861400
##  [253,] 1.75590005 1.90747837
##  [254,] 0.57923065 0.54781504
##  [255,] 0.72680113 1.86764404
##  [256,] 0.33323289 1.35730801
##  [257,] 0.39686886 1.49267739
##  [258,] 0.78507554 0.29047418
##  [259,] 0.63294434 1.57964608
##  [260,] 0.74427504 1.40045218
##  [261,] 0.95042628 1.20374695
##  [262,] 0.67689624 1.19864947
##  [263,] 3.29778206 1.13003296
##  [264,] 0.48571998 3.11591772
##  [265,] 1.00961487 1.20368350
##  [266,] 0.74776760 0.58758669
##  [267,] 0.60830498 0.46892000
##  [268,] 0.39298939 0.32395374
##  [269,] 2.41254304 0.56311216
##  [270,] 0.76649888 0.64792770
##  [271,] 1.44777162 1.23623678
##  [272,] 0.68625651 1.67184844
##  [273,] 2.26060457 0.54780228
##  [274,] 0.76194552 0.74723787
##  [275,] 0.53406993 0.65192174
##  [276,] 0.55040189 2.08996189
##  [277,] 0.60792556 2.20018088
##  [278,] 2.05753013 3.10943812
##  [279,] 1.61741306 1.49968152
##  [280,] 0.25243143 0.79362298
##  [281,] 0.46726798 0.54498052
##  [282,] 0.40588125 0.96795207
##  [283,] 0.49098046 1.68195623
##  [284,] 1.04957831 2.11175990
##  [285,] 0.60389790 0.32433247
##  [286,] 0.65122654 0.68329244
##  [287,] 0.41699221 0.44714007
##  [288,] 0.32505595 1.12659516
##  [289,] 0.49516069 0.16055848
##  [290,] 0.83423055 0.33553603
##  [291,] 0.49708594 0.76162282
##  [292,] 0.54554437 0.51665526
##  [293,] 0.76601091 1.79853529
##  [294,] 0.58600991 0.49513588
##  [295,] 0.72282970 1.43604855
##  [296,] 0.66852566 0.52247993
##  [297,] 0.58374044 0.20475946
##  [298,] 0.56214395 0.78936218
##  [299,] 0.49248126 1.08921951
##  [300,] 0.28821277 1.13941103
##  [301,] 0.66690554 0.39121387
##  [302,] 0.34780347 0.52156095
##  [303,] 0.69494551 1.08021116
##  [304,] 0.92440854 1.46356719
##  [305,] 0.27731993 1.01320311
##  [306,] 0.64824161 0.46749666
##  [307,] 0.92771234 0.28161338
##  [308,] 0.88271790 0.79650325
##  [309,] 0.69379666 0.69722872
##  [310,] 0.25336646 1.16060924
##  [311,] 1.04933003 0.92751052
##  [312,] 2.52930707 0.55543744
##  [313,] 0.38992054 2.17178381
##  [314,] 1.68480173 1.56909621
##  [315,] 0.50903803 1.40699950
##  [316,] 1.15507970 0.64863333
##  [317,] 1.16645056 2.92895877
##  [318,] 0.63477467 1.02760390
##  [319,] 0.92763693 0.60858894
##  [320,] 0.60732215 0.79727683
##  [321,] 0.58788793 0.28440879
##  [322,] 0.41523366 0.77616149
##  [323,] 1.28480290 0.42924820
##  [324,] 1.50298236 1.64495801
##  [325,] 2.89637772 0.70133809
##  [326,] 0.26735897 0.74751968
##  [327,] 0.88704708 2.87636587
##  [328,] 1.42131753 1.34844246
##  [329,] 0.31184429 0.66884777
##  [330,] 1.91904754 0.44344972
##  [331,] 0.99753554 2.05030052
##  [332,] 0.62955764 0.37086328
##  [333,] 0.60448291 0.50261237
##  [334,] 0.79259152 1.06106490
##  [335,] 0.41214555 0.67133370
##  [336,] 0.61263085 1.41487984
##  [337,] 0.87731094 0.57225702
##  [338,] 0.81874805 0.70522569
##  [339,] 1.48401500 0.36733074
##  [340,] 0.80755545 0.41397958
##  [341,] 0.38510410 1.51712350
##  [342,] 0.99674807 1.76946629
##  [343,] 1.31339153 0.96040106
##  [344,] 0.49469628 0.89259935
##  [345,] 0.52094897 1.69591550
##  [346,] 1.27222612 0.46152573
##  [347,] 1.02080389 0.62867695
##  [348,] 0.30484264 0.62122877
##  [349,] 0.63306508 1.07573493
##  [350,] 0.83738553 0.94585578
##  [351,] 0.62619130 1.92878851
##  [352,] 0.31298343 0.69375269
##  [353,] 0.82347745 2.49313360
##  [354,] 0.95463804 2.97604048
##  [355,] 0.72407922 0.55135958
##  [356,] 1.11609505 0.73352306
##  [357,] 3.44777231 0.34669580
##  [358,] 0.47834735 0.66084086
##  [359,] 0.78303378 1.71807414
##  [360,] 0.32122910 2.42458700
##  [361,] 0.84181450 0.71237059
##  [362,] 0.80210709 0.51666830
##  [363,] 0.81418222 0.41973200
##  [364,] 1.72497831 2.07352670
##  [365,] 1.03814228 1.18391635
##  [366,] 1.54806687 0.36436127
##  [367,] 0.51202442 0.45904319
##  [368,] 0.40045773 0.70291434
##  [369,] 0.84458782 0.82197661
##  [370,] 0.97367082 0.61567152
##  [371,] 0.96699024 1.08551915
##  [372,] 0.17856647 2.83833739
##  [373,] 0.48008654 0.32146289
##  [374,] 1.44833382 0.23575595
##  [375,] 0.39010970 0.37461507
##  [376,] 0.81678104 0.68139154
##  [377,] 0.44296002 0.81441756
##  [378,] 0.82049017 0.44269180
##  [379,] 1.33570557 0.75545366
##  [380,] 0.79249464 1.09478492
##  [381,] 0.52666458 0.85710650
##  [382,] 0.49135974 1.51746689
##  [383,] 0.64034687 0.66067410
##  [384,] 0.80354674 2.47717728
##  [385,] 2.86308677 1.32448863
##  [386,] 0.47243203 0.84431754
##  [387,] 0.93358672 0.88082304
##  [388,] 1.81272931 1.84269242
##  [389,] 1.86669875 0.26199345
##  [390,] 1.07814365 2.12153618
##  [391,] 0.48575962 0.50465850
##  [392,] 1.07162932 1.23894078
##  [393,] 1.83439548 1.93168171
##  [394,] 1.17882875 1.41362356
##  [395,] 0.66936578 3.50742940
##  [396,] 1.05996536 0.68570805
##  [397,] 1.19775929 1.31429393
##  [398,] 0.37626893 0.51221054
##  [399,] 2.53432085 0.28415256
##  [400,] 0.56096736 3.60482466
##  [401,] 1.62414561 0.45794788
##  [402,] 0.36267828 1.03745711
##  [403,] 0.34645889 1.68433915
##  [404,] 1.20895301 0.69000710
##  [405,] 1.10253771 1.05761227
##  [406,] 0.30156863 0.98797236
##  [407,] 1.65357020 0.89673554
##  [408,] 0.74559671 0.85946525
##  [409,] 1.88925644 2.24104120
##  [410,] 1.02520576 0.66341055
##  [411,] 0.60145302 0.73049477
##  [412,] 1.11827477 1.53506684
##  [413,] 1.05566319 4.58913632
##  [414,] 0.17242141 0.44858776
##  [415,] 0.45908903 0.73218904
##  [416,] 0.48977344 0.92645937
##  [417,] 2.23149235 0.36812389
##  [418,] 0.31285235 0.90880565
##  [419,] 1.34363004 0.63842169
##  [420,] 0.69250339 0.76727009
##  [421,] 0.48899075 0.76861352
##  [422,] 0.74259006 0.88219283
##  [423,] 1.33527199 1.40886156
##  [424,] 0.99867499 0.37119275
##  [425,] 2.16126145 0.45702919
##  [426,] 0.19765071 0.61767373
##  [427,] 0.68163128 0.34958082
##  [428,] 1.34312027 2.25607176
##  [429,] 0.88335263 1.46561753
##  [430,] 0.71399362 1.04017419
##  [431,] 1.42370523 0.54912514
##  [432,] 0.63568208 1.07427345
##  [433,] 0.71815608 1.54945643
##  [434,] 0.45422756 0.32976681
##  [435,] 0.92296354 0.85964535
##  [436,] 0.43441333 1.07628326
##  [437,] 0.80900696 1.75357181
##  [438,] 0.57427760 0.41143251
##  [439,] 0.62244642 2.29999247
##  [440,] 1.90123213 0.79274341
##  [441,] 2.17606506 1.17479557
##  [442,] 0.54689018 0.88809631
##  [443,] 0.45172703 1.64620325
##  [444,] 0.65899780 0.53142653
##  [445,] 1.08521909 0.74905292
##  [446,] 0.40896226 0.55099418
##  [447,] 0.73942955 0.48262322
##  [448,] 1.02551289 0.55452668
##  [449,] 1.05391834 0.83417667
##  [450,] 2.40346704 0.92343043
##  [451,] 0.57844120 1.15600940
##  [452,] 0.52844143 0.54322493
##  [453,] 0.17205616 1.83504446
##  [454,] 0.09459263 2.77021289
##  [455,] 0.53405051 0.88862402
##  [456,] 1.19764222 0.74351589
##  [457,] 0.77044755 0.82686208
##  [458,] 1.59653471 0.55224479
##  [459,] 0.48730440 0.92050132
##  [460,] 1.18738127 1.05435046
##  [461,] 0.62638347 0.56061081
##  [462,] 1.12436151 0.98027673
##  [463,] 1.54013264 0.82057159
##  [464,] 0.88275831 1.80722483
##  [465,] 0.70415278 1.41776653
##  [466,] 0.86071487 0.68926627
##  [467,] 0.48552644 0.84026444
##  [468,] 0.60597502 0.73618758
##  [469,] 0.56714073 0.75133845
##  [470,] 0.91078763 0.43576405
##  [471,] 0.44939432 0.80551907
##  [472,] 0.39356811 1.00907303
##  [473,] 0.47357436 0.64801981
##  [474,] 1.81331825 0.92665330
##  [475,] 0.76134069 3.23412043
##  [476,] 1.31428440 0.63834443
##  [477,] 0.76891579 1.27137745
##  [478,] 0.25454333 1.94472740
##  [479,] 0.63133280 0.99831714
##  [480,] 0.68720934 0.24410480
##  [481,] 0.66318816 0.22701244
##  [482,] 0.44302593 1.01501448
##  [483,] 0.30616403 1.09490763
##  [484,] 0.42151013 0.32112431
##  [485,] 0.60014280 0.64327638
##  [486,] 0.56300833 2.53817873
##  [487,] 1.21265314 3.43910626
##  [488,] 1.56129160 0.18294372
##  [489,] 1.74926485 1.40529906
##  [490,] 0.71748820 1.39900214
##  [491,] 0.74558396 0.76103704
##  [492,] 0.48369036 0.84506242
##  [493,] 1.04216623 0.46619490
##  [494,] 1.20002874 0.83356382
##  [495,] 0.68809664 0.73706575
##  [496,] 0.27554710 1.17467368
##  [497,] 0.65683496 1.36945157
##  [498,] 0.64476183 0.48060087
##  [499,] 0.42356926 0.50876272
##  [500,] 1.18564039 0.33065664
##  [501,] 0.76626602 0.27755716
##  [502,] 0.70249480 0.30807193
##  [503,] 1.94496530 0.42515698
##  [504,] 0.66998180 1.02576124
##  [505,] 2.09017620 1.66184469
##  [506,] 1.04417641 1.70590211
##  [507,] 0.71201885 1.16407721
##  [508,] 0.63179314 0.67301436
##  [509,] 0.90438679 1.22144693
##  [510,] 1.00115149 0.51938619
##  [511,] 1.64408226 0.82416219
##  [512,] 0.83816620 1.24091680
##  [513,] 0.93163285 1.22625737
##  [514,] 0.66526405 0.97830550
##  [515,] 0.50599047 0.95570469
##  [516,] 0.71922194 0.36975291
##  [517,] 2.19389053 1.46083273
##  [518,] 1.14294169 0.17224780
##  [519,] 1.69383974 0.78112563
##  [520,] 1.59803002 2.20545641
##  [521,] 0.72746997 0.69767579
##  [522,] 1.37058706 0.48516110
##  [523,] 3.00978232 1.56137619
##  [524,] 1.53530687 1.34684086
##  [525,] 0.55438724 0.62455497
##  [526,] 0.56942460 0.80431608
##  [527,] 0.64550457 0.84005619
##  [528,] 1.17945666 0.50267272
##  [529,] 0.70730660 0.82858724
##  [530,] 1.15743555 0.88778387
##  [531,] 0.52361805 1.34814400
##  [532,] 0.92099271 1.04843131
##  [533,] 0.74134619 0.73552035
##  [534,] 0.67190884 0.71611103
##  [535,] 0.65095186 0.72905674
##  [536,] 0.93565960 1.13598518
##  [537,] 0.23336993 0.80966534
##  [538,] 2.35835202 0.71942225
##  [539,] 1.39863584 0.55255354
##  [540,] 0.94713424 1.39090759
##  [541,] 3.92099171 2.78061855
##  [542,] 0.66641418 0.58105406
##  [543,] 0.94833213 0.94061311
##  [544,] 0.29705825 1.33642081
##  [545,] 1.18633659 0.97437109
##  [546,] 0.95644460 2.14304009
##  [547,] 0.80914831 3.14987468
##  [548,] 0.82796226 0.66852143
##  [549,] 1.79749983 2.42183689
##  [550,] 0.62663645 0.88490325
##  [551,] 2.40556195 1.84303916
##  [552,] 1.18982044 1.04021912
##  [553,] 0.39775488 1.19575368
##  [554,] 0.52432322 0.67127851
##  [555,] 1.15318248 1.69251359
##  [556,] 2.18296600 0.53752808
##  [557,] 4.13102346 1.70197601
##  [558,] 2.17649871 0.72211215
##  [559,] 0.20377168 1.03709998
##  [560,] 0.95259520 0.58766366
##  [561,] 0.52947162 0.61135281
##  [562,] 1.64566784 0.37169981
##  [563,] 1.74739788 0.92218326
##  [564,] 1.60149471 0.67464562
##  [565,] 0.02365743 0.91298265
##  [566,] 1.62433692 0.58357452
##  [567,] 1.37888361 1.75506218
##  [568,] 0.72538226 0.45727599
##  [569,] 2.19755833 1.47480402
##  [570,] 3.07522753 1.27631289
##  [571,] 4.44591072 0.44779015
##  [572,] 0.32691821 0.57389267
##  [573,] 1.10622486 1.95364529
##  [574,] 0.40031232 0.64757724
##  [575,] 0.15128045 0.99709993
##  [576,] 0.27144585 0.99946642
##  [577,] 1.03071730 0.59742687
##  [578,] 1.71763165 1.47348008
##  [579,] 0.61436836 1.54184381
##  [580,] 0.76230377 0.53589671
##  [581,] 0.66532317 2.77389912
##  [582,] 0.39630437 0.49760023
##  [583,] 1.18325017 1.09927048
##  [584,] 1.15881916 0.35482996
##  [585,] 0.84125777 1.55033415
##  [586,] 1.39065141 0.43468072
##  [587,] 2.42909785 1.14633856
##  [588,] 1.13883972 1.27810391
##  [589,] 0.49941179 0.87709043
##  [590,] 0.42743054 2.27915542
##  [591,] 2.26103900 1.12723528
##  [592,] 0.20458067 1.07477061
##  [593,] 0.78366404 0.50658212
##  [594,] 0.34227378 0.85099942
##  [595,] 0.87257025 1.00631886
##  [596,] 0.95421036 0.67806871
##  [597,] 2.47364099 1.47278147
##  [598,] 1.04837678 0.68312769
##  [599,] 0.20579166 0.29747308
##  [600,] 1.07421183 1.26781676
##  [601,] 1.54559781 1.11821903
##  [602,] 1.96302786 1.07028532
##  [603,] 1.09971758 2.43182705
##  [604,] 1.67981081 0.63581966
##  [605,] 1.94655164 1.02695859
##  [606,] 0.32025009 1.71948055
##  [607,] 0.74798179 0.96529501
##  [608,] 1.75624331 0.80614725
##  [609,] 0.85550568 0.41347542
##  [610,] 0.70303346 2.13983780
##  [611,] 0.82327709 1.32837650
##  [612,] 1.55207507 0.41181538
##  [613,] 2.23818326 0.77277388
##  [614,] 0.78565677 1.00545515
##  [615,] 1.07261350 0.41592505
##  [616,] 1.11226736 0.32480979
##  [617,] 0.94284955 1.20894126
##  [618,] 2.89324997 0.34861334
##  [619,] 1.03595225 0.78343780
##  [620,] 0.42859559 0.33574687
##  [621,] 2.26505192 0.60960989
##  [622,] 1.05367386 1.19118985
##  [623,] 0.49175009 1.10985201
##  [624,] 1.28555129 1.56699457
##  [625,] 0.68720639 0.72449104
##  [626,] 0.73922983 1.46944839
##  [627,] 0.80539389 1.25585352
##  [628,] 1.71505730 1.03874592
##  [629,] 1.07520388 0.67769984
##  [630,] 0.52976064 0.55418337
##  [631,] 0.27340815 0.47714885
##  [632,] 0.42515395 1.01990714
##  [633,] 1.01992536 4.49308567
##  [634,] 0.61611091 0.54390456
##  [635,] 0.49076362 1.14745949
##  [636,] 0.39033745 0.78129348
##  [637,] 1.87513513 0.57030497
##  [638,] 2.02799544 0.56195892
##  [639,] 1.09939837 2.00885201
##  [640,] 0.33959404 1.96585885
##  [641,] 3.11395069 1.36834991
##  [642,] 0.92576265 1.66914589
##  [643,] 0.55033573 0.52068385
##  [644,] 2.87191750 0.88554952
##  [645,] 0.51782594 0.63645076
##  [646,] 1.17978945 0.96839146
##  [647,] 1.24727452 1.98000850
##  [648,] 0.82066633 0.99774977
##  [649,] 1.15481204 0.68392522
##  [650,] 0.51924193 0.47902329
##  [651,] 0.82277378 0.69023629
##  [652,] 0.39283043 0.87967544
##  [653,] 0.63868216 1.08068832
##  [654,] 1.33001383 0.83013984
##  [655,] 0.88180214 0.30946300
##  [656,] 1.25234865 0.90159587
##  [657,] 1.25845730 0.99572509
##  [658,] 0.49100920 0.14326412
##  [659,] 0.86452144 0.62448252
##  [660,] 0.47336142 0.92227546
##  [661,] 0.95366243 1.04154006
##  [662,] 0.75326482 0.52739361
##  [663,] 0.51048497 0.75434283
##  [664,] 1.33934216 1.15668668
##  [665,] 0.68713763 0.35186455
##  [666,] 0.92816729 1.07064188
##  [667,] 0.54858237 1.04395215
##  [668,] 0.42773534 0.96964888
##  [669,] 0.27992201 0.25426042
##  [670,] 0.30939133 0.92542132
##  [671,] 0.66233151 0.44013025
##  [672,] 0.61847372 1.13383593
##  [673,] 0.68732827 1.16459032
##  [674,] 0.66058907 1.67627585
##  [675,] 1.30591609 0.95922367
##  [676,] 0.74546180 1.10124013
##  [677,] 1.05143138 1.41351577
##  [678,] 1.81372221 1.21088464
##  [679,] 0.43484960 2.54203169
##  [680,] 1.17538069 3.41880590
##  [681,] 0.56313582 0.94280625
##  [682,] 0.30872362 0.56400541
##  [683,] 0.72305923 0.68241921
##  [684,] 0.97489359 0.24327207
##  [685,] 0.98366953 0.58001834
##  [686,] 4.62984173 0.46249814
##  [687,] 0.76845932 1.48443904
##  [688,] 0.62267510 0.68304938
##  [689,] 0.25479680 0.21944705
##  [690,] 1.06405707 0.68326828
##  [691,] 0.68924236 1.21475291
##  [692,] 0.84256625 1.28021901
##  [693,] 0.53946011 0.57769444
##  [694,] 0.45100453 2.86171450
##  [695,] 0.70855891 1.97806735
##  [696,] 0.95381545 0.72539621
##  [697,] 1.20127882 1.20140745
##  [698,] 0.73415845 1.90892220
##  [699,] 0.79285384 1.11965155
##  [700,] 1.46917717 0.45372717
##  [701,] 1.04448632 1.52458807
##  [702,] 0.36200794 0.65525235
##  [703,] 0.51016703 0.72457236
##  [704,] 0.32267376 0.55315977
##  [705,] 1.71697070 0.50234691
##  [706,] 1.42427196 0.59650605
##  [707,] 1.01681958 0.65872191
##  [708,] 0.55341236 2.62275562
##  [709,] 1.38433121 1.28155355
##  [710,] 0.46726267 0.37181688
##  [711,] 0.43250038 0.85676962
##  [712,] 0.54244318 1.26185221
##  [713,] 0.65482474 0.98966029
##  [714,] 0.80213455 1.20133293
##  [715,] 0.60410980 1.36363528
##  [716,] 0.60929269 2.74517755
##  [717,] 0.65998731 0.83682773
##  [718,] 0.76203787 0.55455904
##  [719,] 0.43005870 2.27324622
##  [720,] 1.47500320 2.61622652
##  [721,] 1.48985505 1.56574167
##  [722,] 1.48218712 1.30734662
##  [723,] 0.53804585 1.96204754
##  [724,] 1.74866266 4.64455458
##  [725,] 1.21054205 0.40177484
##  [726,] 1.96617420 0.77683058
##  [727,] 0.31311542 0.72744547
##  [728,] 0.30945494 0.58905209
##  [729,] 0.58203729 1.14435408
##  [730,] 0.35677416 0.86376471
##  [731,] 0.35443035 0.42842719
##  [732,] 0.64878701 1.27751249
##  [733,] 0.53091687 1.43948616
##  [734,] 0.85034167 1.32671994
##  [735,] 0.39863345 0.60843373
##  [736,] 0.81170410 1.36827245
##  [737,] 0.67009454 0.69287715
##  [738,] 0.42731974 0.63331259
##  [739,] 1.32245967 1.91043195
##  [740,] 0.51628874 1.50069308
##  [741,] 0.71002896 2.17552440
##  [742,] 1.28789491 0.50262546
##  [743,] 0.58077105 1.80107869
##  [744,] 0.73495813 0.92168058
##  [745,] 0.88998802 0.53295886
##  [746,] 0.34928720 0.85904279
##  [747,] 0.28059664 0.66313503
##  [748,] 0.80969302 0.48213325
##  [749,] 1.01776289 0.85409912
##  [750,] 0.85740671 0.99809637
##  [751,] 0.73489000 0.44938612
##  [752,] 0.92373100 0.42111202
##  [753,] 1.47178927 0.79670651
##  [754,] 0.82943494 1.18176641
##  [755,] 0.71080895 0.34088550
##  [756,] 1.13784285 1.33457515
##  [757,] 0.83571188 1.10493060
##  [758,] 1.57958734 0.78321726
##  [759,] 0.42345294 0.92130321
##  [760,] 0.62940449 0.72548098
##  [761,] 1.30814866 2.33205705
##  [762,] 0.77454054 1.10292536
##  [763,] 1.40756403 0.99642037
##  [764,] 1.45325955 1.53280667
##  [765,] 1.01501318 2.77405336
##  [766,] 1.06762095 1.38065706
##  [767,] 0.52819477 0.57855194
##  [768,] 0.60428598 0.50227216
##  [769,] 0.80023874 1.44258724
##  [770,] 0.35461246 0.54786371
##  [771,] 0.56235950 1.52272423
##  [772,] 0.47816371 0.61243980
##  [773,] 1.55810647 1.14383038
##  [774,] 1.11052846 1.02813544
##  [775,] 0.66649858 0.28801534
##  [776,] 0.47402627 0.91131822
##  [777,] 1.23882068 1.15409747
##  [778,] 1.45707330 1.33660120
##  [779,] 1.90279063 1.33280970
##  [780,] 1.54804185 0.59218224
##  [781,] 1.10098209 1.76421618
##  [782,] 0.50706905 2.91422902
##  [783,] 0.71496634 0.22146741
##  [784,] 0.98307332 2.50810954
##  [785,] 1.09457465 1.17186721
##  [786,] 0.61594502 1.08426061
##  [787,] 0.93406629 1.00113049
##  [788,] 0.84253889 0.22527246
##  [789,] 1.55665835 2.70224164
##  [790,] 1.44649807 1.90201942
##  [791,] 1.11619320 1.06751457
##  [792,] 0.09383895 0.61235674
##  [793,] 1.47135751 0.60098051
##  [794,] 1.58005465 0.31584613
##  [795,] 1.55739207 0.65692307
##  [796,] 2.29164676 0.55058918
##  [797,] 0.93058450 0.66693521
##  [798,] 0.73500205 0.58323908
##  [799,] 0.67446368 0.94021808
##  [800,] 1.08547387 1.37633270
##  [801,] 0.68245483 0.69545837
##  [802,] 0.50179757 0.62475886
##  [803,] 0.61910098 0.73677167
##  [804,] 1.49026500 0.80969062
##  [805,] 1.45179297 0.89987098
##  [806,] 0.54740790 0.58132030
##  [807,] 0.86205726 0.85138191
##  [808,] 0.59083511 0.52479279
##  [809,] 0.85112129 1.36740351
##  [810,] 0.70658559 0.97233147
##  [811,] 0.81253622 1.15041181
##  [812,] 0.41450782 1.41524205
##  [813,] 0.82091427 0.37259115
##  [814,] 0.52376194 1.41685258
##  [815,] 0.77114039 1.60862863
##  [816,] 1.22465591 0.59073340
##  [817,] 0.95781654 0.95271945
##  [818,] 0.63472191 1.11115609
##  [819,] 0.76358623 1.06704974
##  [820,] 0.59707072 0.71513485
##  [821,] 0.85871503 2.37412511
##  [822,] 0.64158975 0.80347374
##  [823,] 1.55205644 0.35447264
##  [824,] 0.90838222 0.61772986
##  [825,] 3.51577286 1.58348915
##  [826,] 0.33166547 2.33653491
##  [827,] 0.63901842 1.02534814
##  [828,] 0.31128520 5.41353508
##  [829,] 0.51843339 0.97257635
##  [830,] 0.55436876 0.61379923
##  [831,] 0.58574315 1.21869541
##  [832,] 0.29169072 1.28705874
##  [833,] 1.86278887 0.71840808
##  [834,] 0.42041615 0.79215627
##  [835,] 1.02407234 0.73595143
##  [836,] 2.00215929 0.92939937
##  [837,] 0.44559268 0.71634208
##  [838,] 0.89504085 1.65689160
##  [839,] 1.02535354 1.09895574
##  [840,] 0.60917067 1.82510686
##  [841,] 0.69057386 0.26323949
##  [842,] 0.43071677 1.19993542
##  [843,] 1.30753005 0.95535958
##  [844,] 0.13777656 1.44846464
##  [845,] 0.92258916 0.55621499
##  [846,] 0.44873757 1.04286950
##  [847,] 0.64279155 0.79864140
##  [848,] 2.08286281 0.59351539
##  [849,] 0.71094494 1.01808404
##  [850,] 0.48195024 0.93288414
##  [851,] 1.80405854 0.87047101
##  [852,] 2.52854446 1.11100840
##  [853,] 1.21928920 0.70995115
##  [854,] 3.96601672 0.50853007
##  [855,] 2.14479592 1.87646838
##  [856,] 1.90412609 0.18533800
##  [857,] 1.85090905 3.00966631
##  [858,] 0.67214844 4.65391294
##  [859,] 0.70156410 1.01428882
##  [860,] 0.29351715 0.37085724
##  [861,] 1.32320359 0.47168272
##  [862,] 1.27413952 0.55207094
##  [863,] 0.77478015 1.98764433
##  [864,] 3.09711533 1.80370131
##  [865,] 1.01547136 0.74631698
##  [866,] 0.82466584 0.21102808
##  [867,] 0.61803730 2.36629347
##  [868,] 3.46854118 1.11793801
##  [869,] 1.09256390 0.78005281
##  [870,] 0.54059526 0.50013181
##  [871,] 0.32085582 0.60466249
##  [872,] 1.05916034 1.70654660
##  [873,] 1.13585932 1.12630061
##  [874,] 2.21729981 0.58453025
##  [875,] 0.68275123 0.29496890
##  [876,] 2.34421459 0.75510598
##  [877,] 0.96660792 0.76149712
##  [878,] 0.37156579 0.69832164
##  [879,] 0.92663880 0.47332541
##  [880,] 0.31474644 0.62203251
##  [881,] 0.66612502 1.38598333
##  [882,] 0.79651824 0.67247826
##  [883,] 1.87018804 0.13356866
##  [884,] 0.45754262 0.88423297
##  [885,] 0.65014849 0.47032362
##  [886,] 0.77285185 0.86075659
##  [887,] 0.56272327 1.06181624
##  [888,] 0.44374699 2.60851317
##  [889,] 2.04456279 0.59525391
##  [890,] 1.13371743 0.67189767
##  [891,] 1.46390299 1.77383855
##  [892,] 0.13512929 1.72057250
##  [893,] 1.68376913 1.00940365
##  [894,] 0.34731932 1.01305001
##  [895,] 0.65650483 0.52295558
##  [896,] 0.63410093 0.75147133
##  [897,] 0.43276531 0.55611830
##  [898,] 1.17889584 1.29308886
##  [899,] 0.67801612 1.09922046
##  [900,] 1.48300657 0.97460796
##  [901,] 1.25386211 0.38496759
##  [902,] 0.61074999 1.96542454
##  [903,] 0.82498370 0.76577511
##  [904,] 0.30190158 0.58061735
##  [905,] 0.54192490 0.32129647
##  [906,] 0.96739136 0.65171137
##  [907,] 1.20244357 0.54517471
##  [908,] 1.04092612 0.90224335
##  [909,] 0.48427322 1.70539349
##  [910,] 0.37291688 0.60446502
##  [911,] 0.54586214 0.75045415
##  [912,] 0.90915348 0.30176811
##  [913,] 0.93397569 0.45377279
##  [914,] 1.23809691 0.67378531
##  [915,] 0.48201505 0.70064244
##  [916,] 0.84143006 0.80556158
##  [917,] 0.83494952 0.48739706
##  [918,] 0.79742960 0.33584395
##  [919,] 3.93054649 0.83905524
##  [920,] 0.87783594 0.43348257
##  [921,] 0.74400258 0.63340826
##  [922,] 0.32285320 0.81455291
##  [923,] 0.41764934 0.72273306
##  [924,] 1.75716863 1.56628687
##  [925,] 0.54933241 1.35605563
##  [926,] 0.40654202 0.79134487
##  [927,] 0.63489621 1.53863858
##  [928,] 0.51119648 0.29266433
##  [929,] 1.68831206 0.47220610
##  [930,] 0.49666141 0.61521745
##  [931,] 0.65066219 2.64083693
##  [932,] 1.04086558 1.02466130
##  [933,] 1.32745423 1.53111315
##  [934,] 1.64521405 1.40051272
##  [935,] 0.96523879 2.70010459
##  [936,] 0.76993862 0.98871002
##  [937,] 0.52338568 0.54784253
##  [938,] 1.09644134 1.51289873
##  [939,] 2.53652953 0.81627510
##  [940,] 0.75051629 0.35489278
##  [941,] 0.78647710 0.44349760
##  [942,] 1.45006728 1.60062425
##  [943,] 0.65091180 0.42958424
##  [944,] 0.53840189 0.58103261
##  [945,] 1.39281934 2.05964152
##  [946,] 2.65325498 0.52977175
##  [947,] 0.82029603 1.00323597
##  [948,] 1.44925904 0.18480353
##  [949,] 0.52661522 0.74925140
##  [950,] 0.71190988 1.90055415
##  [951,] 0.58813074 0.64582426
##  [952,] 0.45174605 0.22329388
##  [953,] 0.87243712 2.15840187
##  [954,] 1.69847305 1.41647186
##  [955,] 0.57155878 0.57540625
##  [956,] 0.46530578 1.05019750
##  [957,] 0.90364653 0.91433561
##  [958,] 1.49305829 1.07958841
##  [959,] 1.16296979 0.55226303
##  [960,] 2.66687101 0.25149711
##  [961,] 0.48123571 0.37420663
##  [962,] 0.73301988 0.52189599
##  [963,] 0.67200389 0.46139033
##  [964,] 1.05429176 0.53024480
##  [965,] 0.49128965 2.35295215
##  [966,] 1.35870391 0.48767385
##  [967,] 0.74061542 1.94095858
##  [968,] 1.33282109 1.09400639
##  [969,] 1.74403759 2.33643764
##  [970,] 0.25952708 0.61846903
##  [971,] 0.53501305 0.46448707
##  [972,] 0.59442498 1.13909007
##  [973,] 0.47885396 0.16679348
##  [974,] 1.34537240 1.19695725
##  [975,] 0.44915420 0.82809682
##  [976,] 0.64168193 0.52860041
##  [977,] 1.33925002 3.03503864
##  [978,] 0.32839663 1.76664399
##  [979,] 0.98462510 0.85480343
##  [980,] 1.50052079 0.52674144
##  [981,] 0.75205232 0.71317244
##  [982,] 0.39176798 1.71079144
##  [983,] 0.44813997 0.18411487
##  [984,] 0.47527169 2.64295171
##  [985,] 1.66440225 1.57954578
##  [986,] 0.58575582 1.06720555
##  [987,] 1.39610481 0.42259281
##  [988,] 2.61574154 1.33563405
##  [989,] 0.98945853 0.96495544
##  [990,] 0.87999551 1.14208855
##  [991,] 1.02656861 1.18866014
##  [992,] 1.53156084 1.50200472
##  [993,] 0.61494588 0.60978612
##  [994,] 0.86038921 0.64911447
##  [995,] 0.87326882 1.01885810
##  [996,] 0.79084062 0.76181365
##  [997,] 1.04971104 0.36455902
##  [998,] 1.00068603 0.55395156
##  [999,] 0.91927612 0.56423221
## 
## $model.matrix
##    (Intercept) microsite1 shrub_density
## 1            1          1            11
## 2            1          1            12
## 3            1         -1             0
## 4            1         -1             0
## 5            1          1            11
## 6            1          1            10
## 7            1         -1             0
## 8            1         -1             0
## 9            1          1            14
## 10           1          1            13
## 11           1         -1             0
## 12           1         -1             0
## 13           1          1            11
## 14           1          1            11
## 15           1         -1             0
## 16           1         -1             0
## 17           1          1            10
## 18           1          1            11
## 19           1          1            11
## 20           1          1            10
## 21           1         -1             0
## 22           1         -1             0
## 23           1         -1             0
## 24           1         -1             0
## 
## $terms
## pca_data_final ~ microsite * shrub_density
## attr(,"variables")
## list(pca_data_final, microsite, shrub_density)
## attr(,"factors")
##                microsite shrub_density microsite:shrub_density
## pca_data_final         0             0                       0
## microsite              1             0                       1
## shrub_density          0             1                       1
## attr(,"term.labels")
## [1] "microsite"               "shrub_density"          
## [3] "microsite:shrub_density"
## attr(,"order")
## [1] 1 1 2
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## attr(,"class")
## [1] "adonis"
dist_final <- vegdist(pca_data_final, species = "bray")
res_final <- pcoa(dist_final)
p02 <- as.data.frame(res_final$vectors)%>%
  dplyr::select(Axis.1, Axis.2) %>%
  bind_cols(env_final,.)

p02$microsite <- ifelse(p02$microsite == "Density", "Shrub", p02$microsite)

pcoa_final <- ggplot(p02, aes(Axis.1, Axis.2, group = microsite)) +
  geom_point(aes(color = microsite)) +
  geom_text(aes(label=plot), hjust = 0, vjust = 0, check_overlap = TRUE, nudge_x = 0.01)+
  scale_color_brewer(palette = "Set1") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  labs(color = "Microsite")
## Warning: The `size` argument of `element_rect()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
pcoa_final <- pcoa_final + labs(x = "Shrub Density Gradient", y = "Community Composition") + scale_color_manual(
    values = c("Shrub" = "#009900", "Open" = "#0066cc"), # Change color codes here
    labels = c("Shrub" = "Shrub", "Open" = "Open")) + coord_fixed(ratio = 1)
## Scale for colour is already present.
## Adding another scale for colour, which will replace the existing scale.
pcoa_final

model020 <- betadisper(dist_final, env_final$microsite)
model020
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_final, group = env_final$microsite)
## 
## No. of Positive Eigenvalues: 17
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
## Density    Open 
##  0.5034  0.4680 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 23 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.6390 1.2441 0.9185 0.4221 0.3745 0.2048 0.1861 0.1553
anova(model020)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq   Mean Sq F value Pr(>F)
## Groups     1 0.00750 0.0074952  0.2553 0.6184
## Residuals 22 0.64591 0.0293594
permutest(model020,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq   Mean Sq      F N.Perm Pr(>F)
## Groups     1 0.00750 0.0074952 0.2553     99   0.67
## Residuals 22 0.64591 0.0293594                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##         Density Open
## Density         0.66
## Open     0.6184
model020.HSD <- TukeyHSD(model020)
model020.HSD
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = distances ~ group, data = df)
## 
## $group
##                     diff        lwr       upr     p adj
## Open-Density -0.03534393 -0.1804147 0.1097268 0.6183989
boxplot(model020)

model030 <- betadisper(dist_final, env_final$shrub_density)
model030
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_final, group = env_final$shrub_density)
## 
## No. of Positive Eigenvalues: 17
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
##      0     10     11     12     13     14 
## 0.4680 0.3766 0.4847 0.0000 0.0000 0.0000 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 23 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.6390 1.2441 0.9185 0.4221 0.3745 0.2048 0.1861 0.1553
anova(model030)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq Mean Sq F value  Pr(>F)  
## Groups     5 0.58003 0.11601   2.233 0.09554 .
## Residuals 18 0.93511 0.05195                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(model030,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq Mean Sq     F N.Perm Pr(>F)
## Groups     5 0.58003 0.11601 2.233     99    0.1
## Residuals 18 0.93511 0.05195                    
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##          0      10      11 12 13 14
## 0          0.59000 0.82000         
## 10 0.55757         0.66000         
## 11 0.86321 0.60937                 
## 12                                 
## 13                                 
## 14
model030.HSD <- TukeyHSD(model030)
boxplot(model030)

### Shows a significant difference between community composition of tested sites (Carrizo -> Cuyama -> Tecopa)
model040 <- betadisper(dist_final, env_final$site)
model040
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = dist_final, group = env_final$site)
## 
## No. of Positive Eigenvalues: 17
## No. of Negative Eigenvalues: 6
## 
## Average distance to median:
## Carrizo  Cuyama  Tecopa 
##  0.2734  0.3349  0.4558 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 23 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 2.6390 1.2441 0.9185 0.4221 0.3745 0.2048 0.1861 0.1553
anova(model040)
## Analysis of Variance Table
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq F value  Pr(>F)  
## Groups     2 0.13782 0.068911  3.7363 0.04091 *
## Residuals 21 0.38732 0.018444                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(model040,pairwise = TRUE, permutations = 99)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 99
## 
## Response: Distances
##           Df  Sum Sq  Mean Sq      F N.Perm Pr(>F)  
## Groups     2 0.13782 0.068911 3.7363     99   0.03 *
## Residuals 21 0.38732 0.018444                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##          Carrizo   Cuyama Tecopa
## Carrizo          0.410000   0.01
## Cuyama  0.425689            0.12
## Tecopa  0.016550 0.067329
model040.HSD <- TukeyHSD(model040)
supp_plot <- boxplot(model040, xlab = "Region")

### Temperature Data 2022

Temp_2022 <- read_csv("Temp Data 2022.csv")
## Rows: 52443 Columns: 12
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (5): researcher, site, site_code, microsite, time_block
## dbl  (5): microsite_number, pendent_number, pendent_ID, rep, temp
## date (1): date
## time (1): time
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Temp_2022_final <- Temp_2022 %>%
  group_by(site_code, microsite) %>%
  summarise(mean_temp = mean(temp), max_temp = max(temp))
## `summarise()` has grouped output by 'site_code'. You can override using the
## `.groups` argument.
###Ground Temp Data
Ground_Temp_2022 <- read_csv("Gradient Density Datasheet 2022.csv")
## Rows: 695 Columns: 26
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (4): site, site_code, date, microsite
## dbl (22): rep, microsite_number, shrub_ID, shrub_number, total_shrub, micros...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Ground_Temp_2022_final <- Ground_Temp_2022 %>%
  group_by(site_code, microsite) %>%
  summarise(mean_ground_temp = mean(ground_temp), mean_humidity = mean(RH), max_humidity = max(RH), max_ground_temp = max(ground_temp)) 
## `summarise()` has grouped output by 'site_code'. You can override using the
## `.groups` argument.
### Combine this with new_data
### Aridity Data
aridity <- read_csv("regional_sites_2022.csv")
## Rows: 51 Columns: 25
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (17): state, desert, region, experiment, site_acronym, sub_site, site_co...
## dbl  (7): lat, long, elevation, MAT, MAP, aridity, area_block_m2
## num  (1): area_m2
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
aridity <- aridity %>%
 dplyr::select(site_code, aridity)
final_2022<- photo%>%
  group_by(site, site_code, year, microsite, plot, shrub_density, common_name) %>%
  summarise(captures = sum(animal.hit), n = n())
## `summarise()` has grouped output by 'site', 'site_code', 'year', 'microsite',
## 'plot', 'shrub_density'. You can override using the `.groups` argument.
final_2022 <- final_2022 %>%
  filter(common_name != "Blank")%>% filter(common_name != "No CV Result")

density_simple <- final_2022 %>%
  group_by(site, site_code, year, microsite, plot, shrub_density) %>%
  summarise(animals = sum(captures), richness = n()) %>%
 rename(microsite_number = 'plot')
## `summarise()` has grouped output by 'site', 'site_code', 'year', 'microsite',
## 'plot'. You can override using the `.groups` argument.
#write.csv(density_simple, file = "density_simple_fixed.csv") Output density simple because it does not include the sites with 0 observations
density_simple_fixed <- read.csv("density_simple_fixed.csv")
density_simple_fixed <- density_simple_fixed[,-1]
### This is for 2022 evenness
vegan_data <- animals_density ### Created new df for pca data
vegan_data <- vegan_data %>%
  spread(common_name, captures) %>%
  ungroup() %>%
  replace(is.na(.),0)


evenness_data <- vegan_data %>%
  group_by(site_code, microsite) %>%
  summarize(across(5:29, ~diversity(., index = "shannon")))
## `summarise()` has grouped output by 'site_code'. You can override using the
## `.groups` argument.
evenness_data <- na.omit(evenness_data)

evenness_data <- evenness_data %>%
  mutate(Average_Evenness = rowMeans(across(5:26)))

evenness_data <- evenness_data %>%
  dplyr::select(site_code, microsite, Average_Evenness) 
### Join evenness_data with density_simple data
new_data <- inner_join(density_simple_fixed, evenness_data, by = c("site_code", "microsite"))

### Combine new data with logger temp data from 2022
new_data <- inner_join(new_data, Temp_2022_final,by = c("site_code", "microsite"))

### Need to add ground temperature from hand recordings then 2022 is ready!
new_data <- inner_join(new_data, Ground_Temp_2022_final, by = c("site_code", "microsite"))

### Combine all data with aridity data of the sites we have
new_data <- inner_join(new_data, aridity, by = c("site_code"))

### 2022 data is now cleaned and ready to go
### Clean up 2023 data so it can be properly combined with 2022 data

final_2023<- photo_2023%>%
  group_by(site, site_code, year, microsite, plot, shrub_density, common_name) %>%
  summarise(captures = sum(animal.hit), n = n())
## `summarise()` has grouped output by 'site', 'site_code', 'year', 'microsite',
## 'plot', 'shrub_density'. You can override using the `.groups` argument.
density_simple_2023 <- final_2023 %>%
  group_by(site, site_code, year, microsite, plot, shrub_density) %>%
  summarise(animals = sum(captures), richness = n()) %>%
 rename(microsite_number = 'plot')
## `summarise()` has grouped output by 'site', 'site_code', 'year', 'microsite',
## 'plot'. You can override using the `.groups` argument.
write.csv(density_simple_2023, file = "density_simple_fixed_2023.csv")


### This is for 2023 evenness
vegan_data_2023 <- animals_density_2023 ### Created new df for pca data
vegan_data_2023 <- vegan_data_2023 %>%
  spread(common_name, captures) %>%
  ungroup() %>%
  replace(is.na(.),0)

evenness_data_2023 <- vegan_data_2023 %>%
  group_by(site_code, microsite) %>%
  summarize(across(5:27, ~diversity(., index = "shannon")))
## `summarise()` has grouped output by 'site_code'. You can override using the
## `.groups` argument.
evenness_data_2023 <- na.omit(evenness_data_2023)

evenness_data_2023 <- evenness_data_2023 %>%
  mutate(Average_Evenness = rowMeans(across(5:24)))
evenness_data_2023 <- evenness_data_2023 %>%
  dplyr::select(site_code, microsite, Average_Evenness) 
new_data_2023 <- inner_join(density_simple_2023, evenness_data_2023, by = c("site_code", "microsite"))

new_data_2023$site_code <- gsub("Tecopa_Shrub", "Tecopa_shrub", new_data_2023$site_code)
new_data_2023$site_code <- gsub("Tecopa_Open", "Tecopa_open", new_data_2023$site_code)

### Follow same steps as above 2022 data clean up. Start with logger temp, then ground temp, then aridity.

### Combine new_data_2023 to Temp_2023
Temp_2023 <- read_csv("Temp Data 2023.csv") %>% filter(!(temp > 50)) %>% filter(!(temp < -47))
## Rows: 24760 Columns: 11
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (4): researcher, site, site_code, microsite
## dbl  (5): microsite_number, pendant_number, pendant_ID, rep, temp
## date (1): date
## time (1): time
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Temp_2023_final <- Temp_2023 %>%
  group_by(site_code, microsite) %>%
  summarise(mean_temp = mean(temp), max_temp = max(temp))
## `summarise()` has grouped output by 'site_code'. You can override using the
## `.groups` argument.
new_data_2023 <- inner_join(new_data_2023, Temp_2023_final, by = c("site_code", "microsite"))

### Combine Ground Temp Data from 2023
Ground_Temp_2023 <- read_csv("Gradient Density Datasheet 2023.csv")
## New names:
## Rows: 587 Columns: 29
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (4): site, site_code, date, microsite dbl (25): rep, microsite_number,
## shrub_ID, shrub_number, total_shrub, micros...
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `` -> `...28`
## • `` -> `...29`
Ground_Temp_2023_final <- Ground_Temp_2023 %>%
  group_by(site_code, microsite, microsite_number) %>%
  summarise(mean_ground_temp = mean(ground_temp), mean_humidity = mean(RH), max_humidity = max(RH), max_ground_temp = max(ground_temp)) 
## `summarise()` has grouped output by 'site_code', 'microsite'. You can override
## using the `.groups` argument.
new_data_2023 <- inner_join(new_data_2023, Ground_Temp_2023_final, by = c("site_code", "microsite", "microsite_number"))

### Aridity data is already set up from 2022 data
new_data_2023 <- inner_join(new_data_2023, aridity, by = c("site_code"))

### 2023 Data is now cleaned and ready to be combined with 2022 data
final_data <- rbind(new_data, new_data_2023)

All Data is combined now into one clean dataframe that can be used to generate figures and statistics (Use final_data)

Stats for Shrub Density

library(ggpubr)
shapiro.test(final_data$animals)
## 
##  Shapiro-Wilk normality test
## 
## data:  final_data$animals
## W = 0.62948, p-value = 1.551e-09
ggqqplot(final_data$animals)

### Stats to show that the aridity across tested regions significantly varies. This needs to be one of the FIRST things you put in your results.
anova_result <- aov(aridity ~ site, data = final_data)
summary(anova_result)
##             Df Sum Sq Mean Sq F value Pr(>F)    
## site         2 103.52   51.76    3639 <2e-16 ***
## Residuals   43   0.61    0.01                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
emmeans(anova_result, pairwise ~ site)
## $emmeans
##  site    emmean     SE df lower.CL upper.CL
##  Carrizo  3.252 0.0319 43    3.188    3.316
##  Cuyama   3.701 0.0298 43    3.641    3.762
##  Tecopa   0.365 0.0298 43    0.305    0.425
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast         estimate     SE df t.ratio p.value
##  Carrizo - Cuyama   -0.449 0.0436 43 -10.297  <.0001
##  Carrizo - Tecopa    2.887 0.0436 43  66.147  <.0001
##  Cuyama - Tecopa     3.336 0.0422 43  79.126  <.0001
## 
## P value adjustment: tukey method for comparing a family of 3 estimates
tukey_result <- TukeyHSD(anova_result)

# View the Tukey's HSD results
print(tukey_result)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = aridity ~ site, data = final_data)
## 
## $site
##                      diff        lwr        upr p adj
## Cuyama-Carrizo  0.4494073  0.3434585  0.5553561     0
## Tecopa-Carrizo -2.8870527 -2.9930014 -2.7811039     0
## Tecopa-Cuyama  -3.3364600 -3.4388162 -3.2341037     0
### Tukey test shows Cuyama less arid than Carrizo, Carrizo less arid than Tecopa, Cuyama less arid than Tecopa
### Abundance
model1 <- glm(animals~shrub_density*site*year+aridity, family = "gaussian", data = final_data)
model1
## 
## Call:  glm(formula = animals ~ shrub_density * site * year + aridity, 
##     family = "gaussian", data = final_data)
## 
## Coefficients:
##                   (Intercept)                  shrub_density  
##                     7.551e+04                      1.061e+04  
##                    siteCuyama                     siteTecopa  
##                     4.027e+05                     -9.065e+04  
##                          year                        aridity  
##                    -3.736e+01                      3.297e+01  
##      shrub_density:siteCuyama       shrub_density:siteTecopa  
##                    -1.559e+03                     -1.211e+04  
##            shrub_density:year                siteCuyama:year  
##                    -5.245e+00                     -1.991e+02  
##               siteTecopa:year  shrub_density:siteCuyama:year  
##                     4.485e+01                      7.703e-01  
## shrub_density:siteTecopa:year  
##                     5.986e+00  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  33 Residual
## Null Deviance:       765800 
## Residual Deviance: 302900    AIC: 563
anova(model1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                       45     765773              
## shrub_density            1    18242        44     747531 0.1586319    
## site                     2   139832        42     607700 0.0004923 ***
## year                     1   137687        41     470013 0.0001076 ***
## aridity                  1       55        40     469958 0.9380678    
## shrub_density:site       2     3544        38     466414 0.8244495    
## shrub_density:year       1     5580        37     460833 0.4355873    
## site:year                2   155562        35     305272 0.0002090 ***
## shrub_density:site:year  2     2342        33     302929 0.8802245    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e2 <- emmeans(model1, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e2
## $emmeans
##  site    year emmean  SE df lower.CL upper.CL
##  Carrizo 2022   83.8 122 33     -164      332
##  Cuyama  2022  235.1 176 33     -123      593
##  Tecopa  2022   74.6 274 33     -482      631
##  Carrizo 2023   15.7 111 33     -210      242
##  Cuyama  2023  -27.6 176 33     -386      330
##  Tecopa  2023   86.4 274 33     -470      643
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate    SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022   -151.28  73.5 33  -2.057  0.3336
##  Carrizo year2022 - Tecopa year2022      9.25 391.4 33   0.024  1.0000
##  Carrizo year2022 - Carrizo year2023    68.15  54.7 33   1.246  0.8109
##  Carrizo year2022 - Cuyama year2023    111.45  73.5 33   1.516  0.6570
##  Carrizo year2022 - Tecopa year2023     -2.59 391.4 33  -0.007  1.0000
##  Cuyama year2022 - Tecopa year2022     160.53 446.7 33   0.359  0.9991
##  Cuyama year2022 - Carrizo year2023    219.43  87.3 33   2.515  0.1490
##  Cuyama year2022 - Cuyama year2023     262.73  47.9 33   5.480  0.0001
##  Cuyama year2022 - Tecopa year2023     148.70 446.7 33   0.333  0.9994
##  Tecopa year2022 - Carrizo year2023     58.90 378.5 33   0.156  1.0000
##  Tecopa year2022 - Cuyama year2023     102.20 446.7 33   0.229  0.9999
##  Tecopa year2022 - Tecopa year2023     -11.83  48.2 33  -0.245  0.9999
##  Carrizo year2023 - Cuyama year2023     43.30  87.3 33   0.496  0.9960
##  Carrizo year2023 - Tecopa year2023    -70.73 378.5 33  -0.187  1.0000
##  Cuyama year2023 - Tecopa year2023    -114.04 446.7 33  -0.255  0.9998
## 
## P value adjustment: tukey method for comparing a family of 6 estimates
shapiro.test(final_data$richness)
## 
##  Shapiro-Wilk normality test
## 
## data:  final_data$richness
## W = 0.96052, p-value = 0.1201
ggqqplot(final_data$richness)

### Richness Stats
model2 <- glm(richness~shrub_density*site*year +aridity, family = "gaussian", data = final_data)
model2
## 
## Call:  glm(formula = richness ~ shrub_density * site * year + aridity, 
##     family = "gaussian", data = final_data)
## 
## Coefficients:
##                   (Intercept)                  shrub_density  
##                    -1.049e+03                     -9.984e+01  
##                    siteCuyama                     siteTecopa  
##                     1.799e+04                     -6.515e+03  
##                          year                        aridity  
##                     5.227e-01                     -5.391e-01  
##      shrub_density:siteCuyama       shrub_density:siteTecopa  
##                    -2.708e+02                     -1.922e+02  
##            shrub_density:year                siteCuyama:year  
##                     4.939e-02                     -8.895e+00  
##               siteTecopa:year  shrub_density:siteCuyama:year  
##                     3.219e+00                      1.339e-01  
## shrub_density:siteTecopa:year  
##                     9.508e-02  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  33 Residual
## Null Deviance:       575.9 
## Residual Deviance: 79.32     AIC: 183.6
anova_results2 <- aov(model2, test = "Chisq")
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'test' will be disregarded
anova(model2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                       45     575.91              
## shrub_density            1   27.132        44     548.78 0.0007803 ***
## site                     2  164.760        42     384.02 1.305e-15 ***
## year                     1    6.218        41     377.80 0.1077656    
## aridity                  1    1.307        40     376.50 0.4609209    
## shrub_density:site       2    1.941        38     374.56 0.6678024    
## shrub_density:year       1    3.261        37     371.29 0.2441039    
## site:year                2  290.938        35      80.36 < 2.2e-16 ***
## shrub_density:site:year  2    1.034        33      79.32 0.8064261    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(anova_results2)
##                         Df Sum Sq Mean Sq F value   Pr(>F)    
## shrub_density            1  27.13   27.13  11.287  0.00198 ** 
## site                     2 164.76   82.38  34.272 8.82e-09 ***
## year                     1   6.22    6.22   2.587  0.11729    
## aridity                  1   1.31    1.31   0.544  0.46613    
## shrub_density:site       2   1.94    0.97   0.404  0.67106    
## shrub_density:year       1   3.26    3.26   1.357  0.25246    
## site:year                2 290.94  145.47  60.519 9.11e-12 ***
## shrub_density:site:year  2   1.03    0.52   0.215  0.80755    
## Residuals               33  79.32    2.40                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e3 <- emmeans(model2, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e3  ### Ok now this all works.
## $emmeans
##  site    year emmean   SE df lower.CL upper.CL
##  Carrizo 2022  6.356 1.97 33    2.346    10.37
##  Cuyama  2022 12.443 2.85 33    6.649    18.24
##  Tecopa  2022  0.208 4.43 33   -8.799     9.21
##  Carrizo 2023  7.168 1.80 33    3.513    10.82
##  Cuyama  2023  5.146 2.85 33   -0.648    10.94
##  Tecopa  2023  4.797 4.43 33   -4.209    13.80
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate    SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022    -6.087 1.190 33  -5.116  0.0002
##  Carrizo year2022 - Tecopa year2022     6.148 6.333 33   0.971  0.9239
##  Carrizo year2022 - Carrizo year2023   -0.813 0.885 33  -0.918  0.9390
##  Carrizo year2022 - Cuyama year2023     1.210 1.190 33   1.017  0.9090
##  Carrizo year2022 - Tecopa year2023     1.558 6.333 33   0.246  0.9999
##  Cuyama year2022 - Tecopa year2022     12.235 7.229 33   1.692  0.5461
##  Cuyama year2022 - Carrizo year2023     5.274 1.412 33   3.736  0.0085
##  Cuyama year2022 - Cuyama year2023      7.297 0.776 33   9.405  <.0001
##  Cuyama year2022 - Tecopa year2023      7.645 7.229 33   1.058  0.8944
##  Tecopa year2022 - Carrizo year2023    -6.960 6.125 33  -1.136  0.8626
##  Tecopa year2022 - Cuyama year2023     -4.938 7.229 33  -0.683  0.9826
##  Tecopa year2022 - Tecopa year2023     -4.590 0.781 33  -5.880  <.0001
##  Carrizo year2023 - Cuyama year2023     2.022 1.412 33   1.432  0.7076
##  Carrizo year2023 - Tecopa year2023     2.371 6.125 33   0.387  0.9988
##  Cuyama year2023 - Tecopa year2023      0.348 7.229 33   0.048  1.0000
## 
## P value adjustment: tukey method for comparing a family of 6 estimates
ggqqplot(final_data$Average_Evenness)

### Evenness
model3 <- glm(Average_Evenness~shrub_density*site*year + aridity, family = "gaussian", data = final_data)
model3
## 
## Call:  glm(formula = Average_Evenness ~ shrub_density * site * year + 
##     aridity, family = "gaussian", data = final_data)
## 
## Coefficients:
##                   (Intercept)                  shrub_density  
##                     1.175e+02                     -8.606e+00  
##                    siteCuyama                     siteTecopa  
##                     2.013e+02                     -3.866e+02  
##                          year                        aridity  
##                    -5.801e-02                     -2.568e-02  
##      shrub_density:siteCuyama       shrub_density:siteTecopa  
##                     1.008e+01                     -9.806e+00  
##            shrub_density:year                siteCuyama:year  
##                     4.257e-03                     -9.952e-02  
##               siteTecopa:year  shrub_density:siteCuyama:year  
##                     1.911e-01                     -4.981e-03  
## shrub_density:siteTecopa:year  
##                     4.848e-03  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  33 Residual
## Null Deviance:       0.3064 
## Residual Deviance: 0.02358   AIC: -190
anova_results3 <- aov(model3, test = "Chisq")
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'test' will be disregarded
anova(model3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                       45   0.306353              
## shrub_density            1 0.020430        44   0.285923 8.936e-08 ***
## site                     2 0.011457        42   0.274466 0.0003297 ***
## year                     1 0.000058        41   0.274408 0.7763951    
## aridity                  1 0.000022        40   0.274386 0.8618492    
## shrub_density:site       2 0.001475        38   0.272911 0.3562435    
## shrub_density:year       1 0.000932        37   0.271980 0.2535206    
## site:year                2 0.242134        35   0.029845 < 2.2e-16 ***
## shrub_density:site:year  2 0.006265        33   0.023580 0.0124756 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(anova_results3)
##                         Df  Sum Sq Mean Sq F value   Pr(>F)    
## shrub_density            1 0.02043 0.02043  28.592 6.62e-06 ***
## site                     2 0.01146 0.00573   8.017  0.00145 ** 
## year                     1 0.00006 0.00006   0.081  0.77817    
## aridity                  1 0.00002 0.00002   0.030  0.86291    
## shrub_density:site       2 0.00148 0.00074   1.032  0.36746    
## shrub_density:year       1 0.00093 0.00093   1.304  0.26174    
## site:year                2 0.24213 0.12107 169.432  < 2e-16 ***
## shrub_density:site:year  2 0.00627 0.00313   4.384  0.02049 *  
## Residuals               33 0.02358 0.00071                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e4 <- emmeans(model3, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e4  ### Need to double check emmeans it does not match the figure
## $emmeans
##  site    year  emmean     SE df lower.CL upper.CL
##  Carrizo 2022  0.1186 0.0340 33  0.04944    0.188
##  Cuyama  2022  0.2302 0.0491 33  0.13028    0.330
##  Tecopa  2022 -0.0251 0.0763 33 -0.18038    0.130
##  Carrizo 2023  0.0856 0.0310 33  0.02254    0.149
##  Cuyama  2023  0.0684 0.0491 33 -0.03150    0.168
##  Tecopa  2023  0.1615 0.0763 33  0.00617    0.317
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate     SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022   -0.1116 0.0205 33  -5.440  0.0001
##  Carrizo year2022 - Tecopa year2022    0.1437 0.1092 33   1.316  0.7744
##  Carrizo year2022 - Carrizo year2023   0.0330 0.0153 33   2.165  0.2809
##  Carrizo year2022 - Cuyama year2023    0.0502 0.0205 33   2.446  0.1701
##  Carrizo year2022 - Tecopa year2023   -0.0429 0.1092 33  -0.393  0.9987
##  Cuyama year2022 - Tecopa year2022     0.2553 0.1246 33   2.048  0.3384
##  Cuyama year2022 - Carrizo year2023    0.1446 0.0243 33   5.941  <.0001
##  Cuyama year2022 - Cuyama year2023     0.1618 0.0134 33  12.094  <.0001
##  Cuyama year2022 - Tecopa year2023     0.0687 0.1246 33   0.551  0.9934
##  Tecopa year2022 - Carrizo year2023   -0.1106 0.1056 33  -1.048  0.8980
##  Tecopa year2022 - Cuyama year2023    -0.0935 0.1246 33  -0.750  0.9738
##  Tecopa year2022 - Tecopa year2023    -0.1865 0.0135 33 -13.861  <.0001
##  Carrizo year2023 - Cuyama year2023    0.0172 0.0243 33   0.705  0.9800
##  Carrizo year2023 - Tecopa year2023   -0.0759 0.1056 33  -0.719  0.9782
##  Cuyama year2023 - Tecopa year2023    -0.0931 0.1246 33  -0.747  0.9743
## 
## P value adjustment: tukey method for comparing a family of 6 estimates

Data Viz

### All below in chunk are by site

### Abundance vs Density
abundance <- ggplot(final_data, aes(shrub_density, animals, color = site)) +
  geom_point(size = 0.5) +
  facet_wrap(~year)+
  scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + theme(axis.title.x = element_blank()) + labs(tag = "A")+
  labs(x = "Shrub Density (Individuals per 20m radius)", y = "Animal Abundance")
abundance 
## `geom_smooth()` using formula = 'y ~ x'

richness <- ggplot(final_data, aes(shrub_density, richness, color = site)) +
  geom_point(size = 0.5) +
  facet_wrap(~year)+
  scale_color_brewer(palette = "Set1") + theme_classic() +  theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + theme(axis.title.x = element_blank()) + labs(tag = "B")+
  labs(x = "Shrub Density (Individuals per 20m radius)", y = "Richness", color = "Region")
richness
## `geom_smooth()` using formula = 'y ~ x'

Evenness <- ggplot(final_data, aes(shrub_density, Average_Evenness, color = site)) +
  geom_point(size = 0.5) +
  facet_wrap(~year)+
  scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) +  labs(tag = "C")+
  labs(x = expression("Shrub Density per " * 20 * m^2), y = "Mean Evenness")
Evenness
## `geom_smooth()` using formula = 'y ~ x'

library(patchwork)
## 
## Attaching package: 'patchwork'
## 
## The following object is masked from 'package:MASS':
## 
##     area
density_plot <- abundance/richness/Evenness
density_plot
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

### Stats for Average Temperature

### Abundance and temperature
model4 <- glm(animals~mean_temp*site*year*mean_humidity, family = "gaussian", data = final_data) 
model4
## 
## Call:  glm(formula = animals ~ mean_temp * site * year * mean_humidity, 
##     family = "gaussian", data = final_data)
## 
## Coefficients:
##                             (Intercept)  
##                              -6.423e+08  
##                               mean_temp  
##                               2.677e+07  
##                              siteCuyama  
##                               4.148e+08  
##                              siteTecopa  
##                              -4.661e+08  
##                                    year  
##                               3.175e+05  
##                           mean_humidity  
##                               2.602e+07  
##                    mean_temp:siteCuyama  
##                              -1.626e+07  
##                    mean_temp:siteTecopa  
##                               1.146e+07  
##                          mean_temp:year  
##                              -1.323e+04  
##                         siteCuyama:year  
##                              -2.051e+05  
##                         siteTecopa:year  
##                               2.304e+05  
##                 mean_temp:mean_humidity  
##                              -1.084e+06  
##                siteCuyama:mean_humidity  
##                              -1.764e+07  
##                siteTecopa:mean_humidity  
##                              -7.572e+02  
##                      year:mean_humidity  
##                              -1.286e+04  
##               mean_temp:siteCuyama:year  
##                               8.037e+03  
##               mean_temp:siteTecopa:year  
##                              -5.664e+03  
##      mean_temp:siteCuyama:mean_humidity  
##                               6.983e+05  
##      mean_temp:siteTecopa:mean_humidity  
##                               2.925e+01  
##            mean_temp:year:mean_humidity  
##                               5.360e+02  
##           siteCuyama:year:mean_humidity  
##                               8.722e+03  
##           siteTecopa:year:mean_humidity  
##                                      NA  
## mean_temp:siteCuyama:year:mean_humidity  
##                              -3.452e+02  
## mean_temp:siteTecopa:year:mean_humidity  
##                                      NA  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  24 Residual
## Null Deviance:       765800 
## Residual Deviance: 57540     AIC: 504.6
anova_results4 <- aov(model4, test = "Chisq")
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'test' will be disregarded
anova(model4, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                                   Df Deviance Resid. Df Resid. Dev  Pr(>Chi)
## NULL                                                 45     765773          
## mean_temp                          1    69722        44     696052 6.934e-08
## site                               2    82375        42     613676 3.456e-08
## year                               1   184771        41     428905 < 2.2e-16
## mean_humidity                      1     1138        40     427767 0.4907466
## mean_temp:site                     2   108585        38     319182 1.461e-10
## mean_temp:year                     1     7837        37     311345 0.0706052
## site:year                          2    33153        35     278192 0.0009931
## mean_temp:mean_humidity            1      962        34     277230 0.5264108
## site:mean_humidity                 2     5743        32     271487 0.3018453
## year:mean_humidity                 1     7165        31     264322 0.0838464
## mean_temp:site:year                2     6207        29     258114 0.2739932
## mean_temp:site:mean_humidity       2   160588        27      97526 2.845e-15
## mean_temp:year:mean_humidity       1      367        26      97159 0.6956019
## site:year:mean_humidity            1    36297        25      60862 9.978e-05
## mean_temp:site:year:mean_humidity  1     3326        24      57536 0.2388432
##                                      
## NULL                                 
## mean_temp                         ***
## site                              ***
## year                              ***
## mean_humidity                        
## mean_temp:site                    ***
## mean_temp:year                    .  
## site:year                         ***
## mean_temp:mean_humidity              
## site:mean_humidity                   
## year:mean_humidity                .  
## mean_temp:site:year                  
## mean_temp:site:mean_humidity      ***
## mean_temp:year:mean_humidity         
## site:year:mean_humidity           ***
## mean_temp:site:year:mean_humidity    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(anova_results4)
##                              Df Sum Sq Mean Sq F value   Pr(>F)    
## mean_temp                     1  69722   69722  28.639 1.50e-05 ***
## site                          2  82375   41188  16.919 2.26e-05 ***
## year                          1 184771  184771  75.898 4.80e-09 ***
## mean_humidity                 1   1138    1138   0.468 0.500364    
## mean_temp:site                2 108585   54292  22.301 2.76e-06 ***
## mean_temp:year                1   7837    7837   3.219 0.084892 .  
## site:year                     2  33153   16577   6.809 0.004358 ** 
## mean_temp:mean_humidity       1    962     962   0.395 0.535285    
## site:mean_humidity            2   5743    2872   1.180 0.323946    
## year:mean_humidity            1   7165    7165   2.943 0.098614 .  
## mean_temp:site:year           2   6207    3104   1.275 0.297010    
## mean_temp:site:mean_humidity  2 160588   80294  32.982 9.74e-08 ***
## mean_temp:year:mean_humidity  1    367     367   0.151 0.701105    
## site:year:mean_humidity       1  36297   36297  14.910 0.000707 ***
## Residuals                    25  60862    2434                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e5 <- emmeans(model4, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e5
## $emmeans
##  site    year   emmean    SE df lower.CL upper.CL
##  Carrizo 2022   -938.5   619 24    -2217      340
##  Cuyama  2022   1714.0   146 24     1414     2015
##  Tecopa  2022 -89833.5 55883 24  -205170    25503
##  Carrizo 2023     37.5   261 24     -501      576
##  Cuyama  2023   1006.2  1997 24    -3116     5128
##  Tecopa  2023    -81.9  3323 24    -6940     6776
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate    SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022     -2652   636 24  -4.170  0.0041
##  Carrizo year2022 - Tecopa year2022     88895 55335 24   1.606  0.6024
##  Carrizo year2022 - Carrizo year2023     -976   672 24  -1.453  0.6959
##  Carrizo year2022 - Cuyama year2023     -1945  2091 24  -0.930  0.9347
##  Carrizo year2022 - Tecopa year2023      -857  3380 24  -0.253  0.9998
##  Cuyama year2022 - Tecopa year2022      91548 55883 24   1.638  0.5828
##  Cuyama year2022 - Carrizo year2023      1676   299 24   5.615  0.0001
##  Cuyama year2022 - Cuyama year2023        708  2003 24   0.353  0.9992
##  Cuyama year2022 - Tecopa year2023       1796  3326 24   0.540  0.9938
##  Tecopa year2022 - Carrizo year2023    -89871 55876 24  -1.608  0.6012
##  Tecopa year2022 - Cuyama year2023     -90840 55919 24  -1.624  0.5913
##  Tecopa year2022 - Tecopa year2023     -89752 57406 24  -1.563  0.6288
##  Carrizo year2023 - Cuyama year2023      -969  2014 24  -0.481  0.9964
##  Carrizo year2023 - Tecopa year2023       119  3333 24   0.036  1.0000
##  Cuyama year2023 - Tecopa year2023       1088  3877 24   0.281  0.9997
## 
## P value adjustment: tukey method for comparing a family of 6 estimates
### Richness and temperature
model5 <- glm(richness~mean_temp*site*year*mean_humidity, family = "gaussian", data = final_data) 
model5
## 
## Call:  glm(formula = richness ~ mean_temp * site * year * mean_humidity, 
##     family = "gaussian", data = final_data)
## 
## Coefficients:
##                             (Intercept)  
##                               4.250e+05  
##                               mean_temp  
##                              -2.300e+04  
##                              siteCuyama  
##                               8.940e+06  
##                              siteTecopa  
##                               1.097e+05  
##                                    year  
##                              -2.101e+02  
##                           mean_humidity  
##                              -1.721e+04  
##                    mean_temp:siteCuyama  
##                              -3.999e+05  
##                    mean_temp:siteTecopa  
##                               5.848e+03  
##                          mean_temp:year  
##                               1.137e+01  
##                         siteCuyama:year  
##                              -4.421e+03  
##                         siteTecopa:year  
##                              -5.411e+01  
##                 mean_temp:mean_humidity  
##                               9.181e+02  
##                siteCuyama:mean_humidity  
##                              -2.453e+05  
##                siteTecopa:mean_humidity  
##                               4.210e+00  
##                      year:mean_humidity  
##                               8.507e+00  
##               mean_temp:siteCuyama:year  
##                               1.977e+02  
##               mean_temp:siteTecopa:year  
##                              -2.896e+00  
##      mean_temp:siteCuyama:mean_humidity  
##                               1.097e+04  
##      mean_temp:siteTecopa:mean_humidity  
##                              -3.693e-02  
##            mean_temp:year:mean_humidity  
##                              -4.539e-01  
##           siteCuyama:year:mean_humidity  
##                               1.213e+02  
##           siteTecopa:year:mean_humidity  
##                                      NA  
## mean_temp:siteCuyama:year:mean_humidity  
##                              -5.424e+00  
## mean_temp:siteTecopa:year:mean_humidity  
##                                      NA  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  24 Residual
## Null Deviance:       575.9 
## Residual Deviance: 21.07     AIC: 140.6
anova_results5 <- aov(model5, test = "Chisq")
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'test' will be disregarded
anova(model5, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                                   Df Deviance Resid. Df Resid. Dev  Pr(>Chi)
## NULL                                                 45     575.91          
## mean_temp                          1  212.116        44     363.80 < 2.2e-16
## site                               2   13.679        42     350.12 0.0004135
## year                               1  101.722        41     248.40 < 2.2e-16
## mean_humidity                      1   36.989        40     211.41 8.530e-11
## mean_temp:site                     2  105.199        38     106.21 < 2.2e-16
## mean_temp:year                     1   22.336        37      83.87 4.559e-07
## site:year                          2   17.597        35      66.28 4.442e-05
## mean_temp:mean_humidity            1    1.362        34      64.91 0.2129439
## site:mean_humidity                 2    6.395        32      58.52 0.0261978
## year:mean_humidity                 1    0.241        31      58.28 0.6000577
## mean_temp:site:year                2    7.846        29      50.43 0.0114660
## mean_temp:site:mean_humidity       2    3.530        27      46.90 0.1339519
## mean_temp:year:mean_humidity       1   16.254        26      30.65 1.686e-05
## site:year:mean_humidity            1    8.757        25      21.89 0.0015875
## mean_temp:site:year:mean_humidity  1    0.821        24      21.07 0.3334469
##                                      
## NULL                                 
## mean_temp                         ***
## site                              ***
## year                              ***
## mean_humidity                     ***
## mean_temp:site                    ***
## mean_temp:year                    ***
## site:year                         ***
## mean_temp:mean_humidity              
## site:mean_humidity                *  
## year:mean_humidity                   
## mean_temp:site:year               *  
## mean_temp:site:mean_humidity         
## mean_temp:year:mean_humidity      ***
## site:year:mean_humidity           ** 
## mean_temp:site:year:mean_humidity    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(anova_results5)
##                              Df Sum Sq Mean Sq F value   Pr(>F)    
## mean_temp                     1 212.12  212.12 242.238 2.27e-14 ***
## site                          2  13.68    6.84   7.811 0.002316 ** 
## year                          1 101.72  101.72 116.168 6.92e-11 ***
## mean_humidity                 1  36.99   36.99  42.241 8.30e-07 ***
## mean_temp:site                2 105.20   52.60  60.069 2.83e-10 ***
## mean_temp:year                1  22.34   22.34  25.508 3.27e-05 ***
## site:year                     2  17.60    8.80  10.048 0.000627 ***
## mean_temp:mean_humidity       1   1.36    1.36   1.555 0.223910    
## site:mean_humidity            2   6.39    3.20   3.652 0.040617 *  
## year:mean_humidity            1   0.24    0.24   0.276 0.604211    
## mean_temp:site:year           2   7.85    3.92   4.480 0.021736 *  
## mean_temp:site:mean_humidity  2   3.53    1.76   2.015 0.154342    
## mean_temp:year:mean_humidity  1  16.25   16.25  18.563 0.000224 ***
## site:year:mean_humidity       1   8.76    8.76  10.000 0.004075 ** 
## Residuals                    25  21.89    0.88                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e6 <- emmeans(model5, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e6
## $emmeans
##  site    year emmean      SE df  lower.CL upper.CL
##  Carrizo 2022  12.10   11.85 24   -12.360    36.56
##  Cuyama  2022   1.88    2.80 24    -3.898     7.67
##  Tecopa  2022 161.29 1069.41 24 -2045.856  2368.43
##  Carrizo 2023  10.67    4.99 24     0.371    20.97
##  Cuyama  2023 142.87   38.22 24    63.983   221.75
##  Tecopa  2023  33.32   63.59 24   -97.914   164.55
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate      SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022     10.22   12.17 24   0.839  0.9570
##  Carrizo year2022 - Tecopa year2022   -149.19 1058.93 24  -0.141  1.0000
##  Carrizo year2022 - Carrizo year2023     1.43   12.86 24   0.111  1.0000
##  Carrizo year2022 - Cuyama year2023   -130.77   40.02 24  -3.268  0.0340
##  Carrizo year2022 - Tecopa year2023    -21.22   64.68 24  -0.328  0.9994
##  Cuyama year2022 - Tecopa year2022    -159.41 1069.41 24  -0.149  1.0000
##  Cuyama year2022 - Carrizo year2023     -8.79    5.71 24  -1.538  0.6444
##  Cuyama year2022 - Cuyama year2023    -140.98   38.32 24  -3.679  0.0133
##  Cuyama year2022 - Tecopa year2023     -31.44   63.65 24  -0.494  0.9959
##  Tecopa year2022 - Carrizo year2023    150.62 1069.27 24   0.141  1.0000
##  Tecopa year2022 - Cuyama year2023      18.42 1070.09 24   0.017  1.0000
##  Tecopa year2022 - Tecopa year2023     127.97 1098.55 24   0.116  1.0000
##  Carrizo year2023 - Cuyama year2023   -132.19   38.54 24  -3.430  0.0236
##  Carrizo year2023 - Tecopa year2023    -22.65   63.78 24  -0.355  0.9992
##  Cuyama year2023 - Tecopa year2023     109.55   74.19 24   1.477  0.6816
## 
## P value adjustment: tukey method for comparing a family of 6 estimates
### Evenness and temperature
model6 <- glm(Average_Evenness~mean_temp*site*year*mean_humidity, family = "gaussian", data = final_data) 
model6
## 
## Call:  glm(formula = Average_Evenness ~ mean_temp * site * year * mean_humidity, 
##     family = "gaussian", data = final_data)
## 
## Coefficients:
##                             (Intercept)  
##                              -2.924e+04  
##                               mean_temp  
##                               1.075e+03  
##                              siteCuyama  
##                               1.978e+05  
##                              siteTecopa  
##                               1.918e+04  
##                                    year  
##                               1.445e+01  
##                           mean_humidity  
##                               1.089e+03  
##                    mean_temp:siteCuyama  
##                              -8.739e+03  
##                    mean_temp:siteTecopa  
##                              -7.814e+02  
##                          mean_temp:year  
##                              -5.312e-01  
##                         siteCuyama:year  
##                              -9.782e+01  
##                         siteTecopa:year  
##                              -9.486e+00  
##                 mean_temp:mean_humidity  
##                              -3.940e+01  
##                siteCuyama:mean_humidity  
##                              -6.112e+03  
##                siteTecopa:mean_humidity  
##                              -1.112e-02  
##                      year:mean_humidity  
##                              -5.383e-01  
##               mean_temp:siteCuyama:year  
##                               4.321e+00  
##               mean_temp:siteTecopa:year  
##                               3.864e-01  
##      mean_temp:siteCuyama:mean_humidity  
##                               2.686e+02  
##      mean_temp:siteTecopa:mean_humidity  
##                               5.490e-04  
##            mean_temp:year:mean_humidity  
##                               1.948e-02  
##           siteCuyama:year:mean_humidity  
##                               3.022e+00  
##           siteTecopa:year:mean_humidity  
##                                      NA  
## mean_temp:siteCuyama:year:mean_humidity  
##                              -1.328e-01  
## mean_temp:siteTecopa:year:mean_humidity  
##                                      NA  
## 
## Degrees of Freedom: 45 Total (i.e. Null);  24 Residual
## Null Deviance:       0.3064 
## Residual Deviance: 0.001288  AIC: -305.7
anova_results6 <- aov(model6, test = "Chisq")
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'test' will be disregarded
anova(model6, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                                   Df Deviance Resid. Df Resid. Dev  Pr(>Chi)
## NULL                                                 45   0.306353          
## mean_temp                          1 0.011046        44   0.295307 < 2.2e-16
## site                               2 0.073313        42   0.221994 < 2.2e-16
## year                               1 0.068416        41   0.153577 < 2.2e-16
## mean_humidity                      1 0.004958        40   0.148620 < 2.2e-16
## mean_temp:site                     2 0.112108        38   0.036512 < 2.2e-16
## mean_temp:year                     1 0.002065        37   0.034447 5.578e-10
## site:year                          2 0.012030        35   0.022417 < 2.2e-16
## mean_temp:mean_humidity            1 0.000145        34   0.022272 0.1001135
## site:mean_humidity                 2 0.000774        32   0.021498 0.0007366
## year:mean_humidity                 1 0.001450        31   0.020048 2.032e-07
## mean_temp:site:year                2 0.003008        29   0.017040 6.819e-13
## mean_temp:site:mean_humidity       2 0.005407        27   0.011633 < 2.2e-16
## mean_temp:year:mean_humidity       1 0.007064        26   0.004569 < 2.2e-16
## site:year:mean_humidity            1 0.002788        25   0.001781 5.712e-13
## mean_temp:site:year:mean_humidity  1 0.000492        24   0.001288 0.0024604
##                                      
## NULL                                 
## mean_temp                         ***
## site                              ***
## year                              ***
## mean_humidity                     ***
## mean_temp:site                    ***
## mean_temp:year                    ***
## site:year                         ***
## mean_temp:mean_humidity              
## site:mean_humidity                ***
## year:mean_humidity                ***
## mean_temp:site:year               ***
## mean_temp:site:mean_humidity      ***
## mean_temp:year:mean_humidity      ***
## site:year:mean_humidity           ***
## mean_temp:site:year:mean_humidity ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(anova_results6)
##                              Df  Sum Sq Mean Sq F value   Pr(>F)    
## mean_temp                     1 0.01105 0.01105 155.089 3.23e-12 ***
## site                          2 0.07331 0.03666 514.655  < 2e-16 ***
## year                          1 0.06842 0.06842 960.555  < 2e-16 ***
## mean_humidity                 1 0.00496 0.00496  69.605 1.08e-08 ***
## mean_temp:site                2 0.11211 0.05605 786.988  < 2e-16 ***
## mean_temp:year                1 0.00206 0.00206  28.990 1.38e-05 ***
## site:year                     2 0.01203 0.00602  84.452 7.58e-12 ***
## mean_temp:mean_humidity       1 0.00015 0.00015   2.038 0.165804    
## site:mean_humidity            2 0.00077 0.00039   5.437 0.010954 *  
## year:mean_humidity            1 0.00145 0.00145  20.352 0.000132 ***
## mean_temp:site:year           2 0.00301 0.00150  21.114 4.26e-06 ***
## mean_temp:site:mean_humidity  2 0.00541 0.00270  37.958 2.66e-08 ***
## mean_temp:year:mean_humidity  1 0.00706 0.00706  99.178 3.48e-10 ***
## site:year:mean_humidity       1 0.00279 0.00279  39.150 1.52e-06 ***
## Residuals                    25 0.00178 0.00007                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e7 <- emmeans(model6, pairwise~site*year)
## NOTE: Results may be misleading due to involvement in interactions
e7
## $emmeans
##  site    year  emmean     SE df lower.CL upper.CL
##  Carrizo 2022  0.2333 0.0927 24   0.0420   0.4246
##  Cuyama  2022 -0.0603 0.0218 24  -0.1054  -0.0153
##  Tecopa  2022 -0.0817 8.3624 24 -17.3409  17.1775
##  Carrizo 2023  0.0399 0.0390 24  -0.0407   0.1204
##  Cuyama  2023  2.0244 0.2989 24   1.4075   2.6413
##  Tecopa  2023 -0.0993 0.4972 24  -1.1255   0.9269
## 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                            estimate     SE df t.ratio p.value
##  Carrizo year2022 - Cuyama year2022    0.2937 0.0952 24   3.084  0.0508
##  Carrizo year2022 - Tecopa year2022    0.3150 8.2805 24   0.038  1.0000
##  Carrizo year2022 - Carrizo year2023   0.1935 0.1005 24   1.924  0.4125
##  Carrizo year2022 - Cuyama year2023   -1.7911 0.3129 24  -5.724  0.0001
##  Carrizo year2022 - Tecopa year2023    0.3326 0.5058 24   0.658  0.9849
##  Cuyama year2022 - Tecopa year2022     0.0213 8.3625 24   0.003  1.0000
##  Cuyama year2022 - Carrizo year2023   -0.1002 0.0447 24  -2.241  0.2565
##  Cuyama year2022 - Cuyama year2023    -2.0848 0.2997 24  -6.957  <.0001
##  Cuyama year2022 - Tecopa year2023     0.0390 0.4977 24   0.078  1.0000
##  Tecopa year2022 - Carrizo year2023   -0.1215 8.3614 24  -0.015  1.0000
##  Tecopa year2022 - Cuyama year2023    -2.1061 8.3678 24  -0.252  0.9998
##  Tecopa year2022 - Tecopa year2023     0.0176 8.5903 24   0.002  1.0000
##  Carrizo year2023 - Cuyama year2023   -1.9846 0.3014 24  -6.584  <.0001
##  Carrizo year2023 - Tecopa year2023    0.1392 0.4987 24   0.279  0.9997
##  Cuyama year2023 - Tecopa year2023     2.1237 0.5801 24   3.661  0.0139
## 
## P value adjustment: tukey method for comparing a family of 6 estimates
### Ambient Temperature Plots

### Plots of temp might look super ugly.

abundance_temp <- ggplot(final_data, aes(mean_temp, animals)) +
  geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free")+ 
  scale_color_brewer(palette = "Set1") +
  labs(x = "Average Temperature (C)", y = "Animal Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none",legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + theme(axis.title.x = element_blank()) + labs(tag = "A")
abundance_temp
## `geom_smooth()` using formula = 'y ~ x'

richness_temp <- ggplot(final_data, aes(mean_temp, richness)) +
  geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free")+
  scale_color_brewer(palette = "Set1") + theme(axis.title.x = element_blank()) + labs(tag = "B")+ theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none",legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) +
  labs(x = "Average Temperature (C)", y = "Richness") + theme(axis.title.x = element_blank())
richness_temp
## `geom_smooth()` using formula = 'y ~ x'

evenness_temp <- ggplot(final_data, aes(mean_temp, Average_Evenness)) +
  geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free")+
  scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) +  labs(tag = "C")+
  labs(x = expression("Mean Temperature (°C)"), y = "Mean Evenness")
evenness_temp
## `geom_smooth()` using formula = 'y ~ x'

temp_plot <- abundance_temp/richness_temp/evenness_temp
temp_plot
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

### Other posisble figure options

abundance_2 <- ggplot(final_data, aes(shrub_density, animals)) + geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free") + scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + theme(axis.title.x = element_blank()) + labs(tag = "A")+
  labs(x = "Shrub Density (Individuals per 20m radius)", y = "Animal Abundance")
abundance_2
## `geom_smooth()` using formula = 'y ~ x'

richness_2 <- ggplot(final_data, aes(shrub_density, richness)) + geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free") + scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + theme(axis.title.x = element_blank()) + labs(tag = "B")+
  labs(x = "Shrub Density (Individuals per 20m radius)", y = "Richness")
richness_2
## `geom_smooth()` using formula = 'y ~ x'

evenness_2 <- ggplot(final_data, aes(shrub_density, Average_Evenness)) + geom_point(size = 0.5) +
  facet_wrap(~year, scales = "free") + scale_color_brewer(palette = "Set1") + theme_classic() + theme(legend.position = "none") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5),legend.position = "none", legend.title = element_blank(), axis.text = element_text(size = 10)) +
  geom_smooth(method = lm, se = TRUE) + labs(tag = "C")+
  labs(x = expression("Shrub Density per " * 20 * m^2), y = "Mean Evenness")

plot1.1 <- abundance_2/richness_2/evenness_2
plot1.1
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

### Percent proportion Figure
#write.csv(density_obvs_final, file = "Animal Observations.csv")
scientific_names <- read.csv("Animal Observations.csv")
plot3 <- ggplot(scientific_names, aes(scientific_name, percent_presence, fill = microsite)) + geom_bar(stat = "identity") + coord_flip() + theme_classic() + scale_x_discrete(limits=rev) + xlab("Species") + ylab("Percent Proportion") + labs(fill = "Microsite")
plot3 <-plot3 + scale_fill_manual(values = c("#009900", "#0066cc"))
# Assuming you have a dataset named scientific_names with columns: scientific_name, percent_presence, microsite

# Create a new variable to specify the ordering based on presence in density or open areas
scientific_names$microsite <- ifelse(scientific_names$microsite == "Density", "Shrub", scientific_names$microsite)

scientific_names <- scientific_names %>%
  mutate(ordering_var = ifelse(microsite == "Shrub", 1, 2)) %>%
  arrange(ordering_var, desc(percent_presence))



# Create the histogram-style figure with reordering
plot3.2 <- ggplot(scientific_names, aes(fct_inorder(scientific_name), percent_presence, fill = microsite)) +
  geom_bar(stat = "identity") +
  coord_flip() +
  theme_classic() +
  xlab("Species") +
  ylab("Percent Proportion") +
  labs(fill = "Microsite") +
  scale_fill_manual(values = c("#0066cc", "#009900")) + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) 

# Reorder the x-axis labels
plot3.2 <- plot3.2 + scale_x_discrete(limits = rev(levels(scientific_names$scientific_name))) 

# Plot the figure
print(plot3.2)

Final Figures for Publication

### Figure 1: Abundance, Richness, Evenness vs Shrub Density
plot1.1
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

### Figure 2: Abundance, Richness, Evenness vs Average Temperature
temp_plot
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

### Figure 3: PCOA of Communities
pcoa_final

### Figure 4: Percent Proportion of Vertebrate species
plot3.2

#write.csv(final_data, file = "Final Data.csv")

Data Together

### Test figure with formula (Shrub Density)
final_data <- final_data %>%
  mutate(year = as.character(year))

### Density v abundance
ggplot(final_data, aes(shrub_density, animals, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Animal Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "A")

### Density v Richness
ggplot(final_data, aes(shrub_density, richness, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Richness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "B")

### Density v Evenness
ggplot(final_data, aes(shrub_density, Average_Evenness, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Evenness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "C")

### Aridity v Abundance
ggplot(final_data, aes(aridity, animals, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Aridity", y = "Animal Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "A")

### Aridity v Richness
ggplot(final_data, aes(aridity, richness, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Aridity", y = "Richness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "B")

### Aridity v Evenness
ggplot(final_data, aes(aridity, Average_Evenness, color = year)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
scale_color_brewer(palette = "Set1") +  labs(x = "Aridity", y = "Evenness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "C")

### Stats
#install.packages("lme4", type = "source")
library(lmerTest)
## Loading required package: lme4
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## 
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
## 
##     lmer
## The following object is masked from 'package:stats':
## 
##     step
library(performance)
#simple
m1 <- lmer(animals ~ shrub_density + (1|year) + aridity, data = final_data)
check_collinearity(m1)
## # Check for Multicollinearity
## 
## Low Correlation
## 
##           Term  VIF       VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  shrub_density 1.01 [1.00, 2.65e+12]         1.00      0.99     [0.00, 1.00]
##        aridity 1.01 [1.00, 2.65e+12]         1.00      0.99     [0.00, 1.00]
anova(m1)
## Type III Analysis of Variance Table with Satterthwaite's method
##               Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)   
## shrub_density  14370   14370     1 42.018  1.2164 0.27635   
## aridity       114226  114226     1 42.010  9.6692 0.00336 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lsmeansLT(m1)
## Least Squares Means table:
## 
##      Estimate Std. Error df t value lower upper Pr(>|t|)
## 
##   Confidence level: 95%
##   Degrees of freedom method: Satterthwaite
ranova(m1) # I think this is to test for random effects across year?
## ANOVA-like table for random-effects: Single term deletions
## 
## Model:
## animals ~ shrub_density + aridity + (1 | year)
##            npar  logLik    AIC    LRT Df Pr(>Chisq)  
## <none>        5 -271.70 553.40                       
## (1 | year)    4 -274.97 557.94 6.5368  1    0.01057 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m2 <- lmer(richness ~ shrub_density + (1|year) + aridity, data = final_data)
## boundary (singular) fit: see help('isSingular')
check_collinearity(m2)
## # Check for Multicollinearity
## 
## Low Correlation
## 
##           Term  VIF       VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  shrub_density 1.01 [1.00, 7.65e+12]         1.00      0.99     [0.00, 1.00]
##        aridity 1.01 [1.00, 7.65e+12]         1.00      0.99     [0.00, 1.00]
anova(m2)
## Type III Analysis of Variance Table with Satterthwaite's method
##                Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
## shrub_density  17.096  17.096     1    43  1.8397 0.1820664    
## aridity       149.184 149.184     1    43 16.0534 0.0002401 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ranova(m2)
## ANOVA-like table for random-effects: Single term deletions
## 
## Model:
## richness ~ shrub_density + aridity + (1 | year)
##            npar  logLik    AIC         LRT Df Pr(>Chisq)
## <none>        5 -116.83 243.66                          
## (1 | year)    4 -116.83 241.66 -8.5265e-14  1          1
m3 <- lmer(Average_Evenness ~ shrub_density + (1|year) + aridity, data = final_data)
## boundary (singular) fit: see help('isSingular')
check_collinearity(m3)
## # Check for Multicollinearity
## 
## Low Correlation
## 
##           Term  VIF       VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  shrub_density 1.01 [1.00, 7.65e+12]         1.00      0.99     [0.00, 1.00]
##        aridity 1.01 [1.00, 7.65e+12]         1.00      0.99     [0.00, 1.00]
anova(m3)
## Type III Analysis of Variance Table with Satterthwaite's method
##                  Sum Sq   Mean Sq NumDF DenDF F value Pr(>F)  
## shrub_density 0.0215532 0.0215532     1    43  3.2712 0.0775 .
## aridity       0.0026079 0.0026079     1    43  0.3958 0.5326  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ranova(m3)
## ANOVA-like table for random-effects: Single term deletions
## 
## Model:
## Average_Evenness ~ shrub_density + aridity + (1 | year)
##            npar logLik     AIC         LRT Df Pr(>Chisq)
## <none>        5 39.082 -68.164                          
## (1 | year)    4 39.082 -70.164 -1.4211e-14  1          1

Test Trophic Level?

trophic <- read.csv("Animal Observations.csv")


ggplot(trophic, aes(microsite, captures, color = Trophic)) +
geom_boxplot() +
scale_color_brewer(palette = "Set1") +  labs(x = "Aridity", y = "Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "C")

m9<- glm(total ~ microsite * Trophic, family = "poisson", data = trophic)
anova(m9, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: total
## 
## Terms added sequentially (first to last)
## 
## 
##                   Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                 55      27821              
## microsite          1     29.6        54      27791 5.449e-08 ***
## Trophic            2   7884.0        52      19907 < 2.2e-16 ***
## microsite:Trophic  2      2.0        50      19905     0.376    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
e9 <- emmeans(m9, pairwise~microsite|Trophic)
e9
## $emmeans
## Trophic = Carnivore:
##  microsite emmean     SE  df asymp.LCL asymp.UCL
##  Density     3.06 0.0767 Inf      2.91      3.21
##  Open        3.18 0.0769 Inf      3.03      3.33
## 
## Trophic = Herbivore:
##  microsite emmean     SE  df asymp.LCL asymp.UCL
##  Density     5.62 0.0173 Inf      5.59      5.66
##  Open        5.71 0.0174 Inf      5.68      5.74
## 
## Trophic = Omnivore:
##  microsite emmean     SE  df asymp.LCL asymp.UCL
##  Density     3.06 0.0685 Inf      2.92      3.19
##  Open        3.00 0.0788 Inf      2.85      3.16
## 
## Results are given on the log (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
## Trophic = Carnivore:
##  contrast       estimate     SE  df z.ratio p.value
##  Density - Open  -0.1276 0.1086 Inf  -1.175  0.2400
## 
## Trophic = Herbivore:
##  contrast       estimate     SE  df z.ratio p.value
##  Density - Open  -0.0849 0.0245 Inf  -3.461  0.0005
## 
## Trophic = Omnivore:
##  contrast       estimate     SE  df z.ratio p.value
##  Density - Open   0.0567 0.1044 Inf   0.543  0.5869
## 
## Results are given on the log (not the response) scale.

Seperate everything by year (Nonlinear better for 2022)

final_data_2022 <- final_data %>%
  filter(year == "2022")

shapiro.test(final_data_2022$animals)
## 
##  Shapiro-Wilk normality test
## 
## data:  final_data_2022$animals
## W = 0.76017, p-value = 7.037e-05
ggqqplot(final_data_2022$animals)

n1 <- glm(animals ~ shrub_density * aridity, family = "gaussian", data = final_data_2022)
n1
## 
## Call:  glm(formula = animals ~ shrub_density * aridity, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##              -27.7891                 0.6522                54.0811  
## shrub_density:aridity  
##                1.6648  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  20 Residual
## Null Deviance:       619900 
## Residual Deviance: 376700    AIC: 310
anova(n1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     23     619927              
## shrub_density          1    26978        22     592949 0.2314117    
## aridity                1   211738        21     381211 0.0008004 ***
## shrub_density:aridity  1     4465        20     376746 0.6263640    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(n1), "\n")
## Linear Model AIC: 309.9796
quadratic_model_1 <- glm(animals ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", data = final_data_2022)
quadratic_model_1
## 
## Call:  glm(formula = animals ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##               139.405                100.932                 -9.768  
##               aridity           I(aridity^2)  shrub_density:aridity  
##              -412.549                117.917                  6.412  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  18 Residual
## Null Deviance:       619900 
## Residual Deviance: 186500    AIC: 297.1
anova(quadratic_model_1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                                     23     619927             
## shrub_density          1    26978        22     592949 0.106605    
## I(shrub_density^2)     1     2942        21     590007 0.594141    
## aridity                1   261283        20     328724 5.12e-07 ***
## I(aridity^2)           1    89956        19     238768 0.003213 ** 
## shrub_density:aridity  1    52272        18     186496 0.024696 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_1), "\n")
## Quadratic Model AIC: 297.1038
if (AIC(quadratic_model_1) < AIC(n1)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Quadratic model is better.
abund_dens_2022 <- ggplot(final_data_2022, aes(shrub_density, animals)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Animal Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "A") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))

### Richness
n2 <- glm(richness ~ shrub_density * aridity, family = "gaussian", data = final_data_2022)
n2
## 
## Call:  glm(formula = richness ~ shrub_density * aridity, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##              -0.34946                0.08662                2.58054  
## shrub_density:aridity  
##              -0.01174  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  20 Residual
## Null Deviance:       475 
## Residual Deviance: 132.4     AIC: 119.1
anova(n2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     23     474.96              
## shrub_density          1     6.43        22     468.53    0.3243    
## aridity                1   335.94        21     132.58 1.043e-12 ***
## shrub_density:aridity  1     0.22        20     132.36    0.8546    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(n2), "\n")
## Linear Model AIC: 119.0888
quadratic_model_2 <- glm(richness ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", data = final_data_2022)
quadratic_model_2
## 
## Call:  glm(formula = richness ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##                1.9865                -0.7054                 0.0776  
##               aridity           I(aridity^2)  shrub_density:aridity  
##               -3.8810                 1.6566                -0.0559  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  18 Residual
## Null Deviance:       475 
## Residual Deviance: 87.2  AIC: 113.1
anova(quadratic_model_2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     23     474.96              
## shrub_density          1    6.431        22     468.53   0.24925    
## I(shrub_density^2)     1  106.430        21     362.10 2.769e-06 ***
## aridity                1  247.045        20     115.05 9.248e-13 ***
## I(aridity^2)           1   23.883        19      91.17   0.02639 *  
## shrub_density:aridity  1    3.972        18      87.20   0.36517    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_2), "\n")
## Quadratic Model AIC: 113.0717
if (AIC(quadratic_model_2) < AIC(n2)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Quadratic model is better.
rich_dens_2022 <- ggplot(final_data_2022, aes(shrub_density, richness)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Richness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "B") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))

### Evenness
n3 <- glm(Average_Evenness ~ shrub_density * aridity, data = final_data_2022)
n3
## 
## Call:  glm(formula = Average_Evenness ~ shrub_density * aridity, data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##              0.019618              -0.001800               0.030276  
## shrub_density:aridity  
##              0.001651  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  20 Residual
## Null Deviance:       0.1455 
## Residual Deviance: 0.05188   AIC: -69.18
anova(n3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     23   0.145519              
## shrub_density          1 0.007333        22   0.138186    0.0927 .  
## aridity                1 0.081917        21   0.056269 1.913e-08 ***
## shrub_density:aridity  1 0.004391        20   0.051878    0.1932    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(n3), "\n")
## Linear Model AIC: -69.17676
quadratic_model_3 <- glm(Average_Evenness ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", data = final_data_2022)
quadratic_model_3
## 
## Call:  glm(formula = Average_Evenness ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##             0.0446964             -0.0295177              0.0027085  
##               aridity           I(aridity^2)  shrub_density:aridity  
##            -0.0385879              0.0178654              0.0002091  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  18 Residual
## Null Deviance:       0.1455 
## Residual Deviance: 0.03225   AIC: -76.59
anova(quadratic_model_3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     23   0.145519              
## shrub_density          1 0.007333        22   0.138186   0.04307 *  
## I(shrub_density^2)     1 0.056383        21   0.081804 2.027e-08 ***
## aridity                1 0.047100        20   0.034703 2.941e-07 ***
## I(aridity^2)           1 0.002397        19   0.032306   0.24743    
## shrub_density:aridity  1 0.000056        18   0.032251   0.86020    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_2), "\n")
## Quadratic Model AIC: 113.0717
if (AIC(quadratic_model_2) < AIC(n2)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Quadratic model is better.
even_dens_2022 <- ggplot(final_data_2022, aes(shrub_density, Average_Evenness)) +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density per 20m Radius", y = "Evenness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10))+
   labs(tag = "C") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))

plot <- abund_dens_2022/rich_dens_2022/even_dens_2022
plot

### Temperature (Hold off on this and ask chris)

t1 <- glm(animals ~ shrub_density * mean_temp, family = "gaussian", data = final_data_2022)
t1
## 
## Call:  glm(formula = animals ~ shrub_density * mean_temp, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##             (Intercept)            shrub_density                mean_temp  
##                641.3669                  22.3664                 -20.8447  
## shrub_density:mean_temp  
##                 -0.6221  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  20 Residual
## Null Deviance:       619900 
## Residual Deviance: 389100    AIC: 310.8
anova(t1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                                       23     619927            
## shrub_density            1    26978        22     592949 0.238985   
## mean_temp                1   199846        21     393103 0.001351 **
## shrub_density:mean_temp  1     3970        20     389134 0.651496   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(t1), "\n")
## Linear Model AIC: 310.756
quadratic_temp_1 <- glm(animals ~ shrub_density + I(shrub_density^2) + mean_temp + I(mean_temp^2) + shrub_density:mean_temp, family = "gaussian", data = final_data_2022)
quadratic_temp_1
## 
## Call:  glm(formula = animals ~ shrub_density + I(shrub_density^2) + 
##     mean_temp + I(mean_temp^2) + shrub_density:mean_temp, family = "gaussian", 
##     data = final_data_2022)
## 
## Coefficients:
##             (Intercept)            shrub_density       I(shrub_density^2)  
##                4363.574                  155.190                   -6.801  
##               mean_temp           I(mean_temp^2)  shrub_density:mean_temp  
##                -305.916                    5.317                   -2.618  
## 
## Degrees of Freedom: 23 Total (i.e. Null);  18 Residual
## Null Deviance:       619900 
## Residual Deviance: 301200    AIC: 308.6
anova(quadratic_temp_1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                       23     619927              
## shrub_density            1    26978        22     592949 0.2042037    
## I(shrub_density^2)       1     2942        21     590007 0.6750263    
## mean_temp                1   240180        20     349827 0.0001516 ***
## I(mean_temp^2)           1     2772        19     347055 0.6840117    
## shrub_density:mean_temp  1    45820        18     301235 0.0979909 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_temp_1), "\n")
## Quadratic Model AIC: 308.6113

Shrub Density 2023 (Linear better for 2023)

final_data_2023 <- final_data %>%
  filter(year == "2023")

x1 <- glm(animals ~ shrub_density * aridity, family = "gaussian", data = final_data_2023)
x1
## 
## Call:  glm(formula = animals ~ shrub_density * aridity, family = "gaussian", 
##     data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##               8.32431                1.85904                2.30955  
## shrub_density:aridity  
##              -0.05488  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  18 Residual
## Null Deviance:       12650 
## Residual Deviance: 10190     AIC: 207.5
anova(x1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                                     21      12649           
## shrub_density          1  2257.72        20      10391  0.04579 *
## aridity                1   199.04        19      10192  0.55317  
## shrub_density:aridity  1     4.64        18      10187  0.92782  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(x1), "\n")
## Linear Model AIC: 207.4663
quadratic_model_x1 <- glm(animals ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", data = final_data_2023)
quadratic_model_x1
## 
## Call:  glm(formula = animals ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, family = "gaussian", 
##     data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##              -1.65760                3.43942               -0.15541  
##               aridity           I(aridity^2)  shrub_density:aridity  
##              29.97243               -7.06338                0.03991  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  16 Residual
## Null Deviance:       12650 
## Residual Deviance: 9619  AIC: 210.2
anova(quadratic_model_x1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: animals
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                                     21    12648.8           
## shrub_density          1  2257.72        20    10391.1  0.05264 .
## I(shrub_density^2)     1    55.46        19    10335.6  0.76135  
## aridity                1   317.46        18    10018.1  0.46743  
## I(aridity^2)           1   396.75        17     9621.4  0.41659  
## shrub_density:aridity  1     1.93        16     9619.5  0.95482  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_x1), "\n")
## Quadratic Model AIC: 210.2043
if (AIC(quadratic_model_x1) < AIC(x1)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Linear model is better or equally good.
abund_dens_2023 <- ggplot(final_data_2023, aes(shrub_density, animals)) +
geom_smooth(method = "lm", se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Animal Abundance") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "A") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))
abund_dens_2023
## `geom_smooth()` using formula = 'y ~ x'

x2 <- glm(richness ~ shrub_density * aridity, data = final_data_2023)
x2
## 
## Call:  glm(formula = richness ~ shrub_density * aridity, data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##              4.775057               0.220144              -0.167510  
## shrub_density:aridity  
##             -0.009058  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  18 Residual
## Null Deviance:       95.32 
## Residual Deviance: 67.28     AIC: 97.03
anova(x2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                                     21     95.318            
## shrub_density          1  25.4984        20     69.820 0.009006 **
## aridity                1   2.4110        19     67.409 0.421898   
## shrub_density:aridity  1   0.1265        18     67.282 0.854019   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(x2), "\n")
## Linear Model AIC: 97.02606
quadratic_model_x2 <- glm(richness ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, data = final_data_2023)
quadratic_model_x2
## 
## Call:  glm(formula = richness ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##               3.32139               -0.05358                0.02657  
##               aridity           I(aridity^2)  shrub_density:aridity  
##               3.87515               -1.02486               -0.02127  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  16 Residual
## Null Deviance:       95.32 
## Residual Deviance: 59.25     AIC: 98.23
anova(quadratic_model_x2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: richness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                                     21     95.318            
## shrub_density          1  25.4984        20     69.820 0.008689 **
## I(shrub_density^2)     1   0.4031        19     69.417 0.741448   
## aridity                1   2.0180        18     67.399 0.460389   
## I(aridity^2)           1   7.6014        17     59.797 0.151936   
## shrub_density:aridity  1   0.5479        16     59.249 0.700486   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_x2), "\n")
## Quadratic Model AIC: 98.22897
if (AIC(quadratic_model_x2) < AIC(x2)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Linear model is better or equally good.
rich_dens_2023 <- ggplot(final_data_2023, aes(shrub_density, richness)) +
geom_smooth(method = "lm", se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density 20m Radius", y = "Richness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) +
  theme(axis.title.x = element_blank()) + labs(tag = "B") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))
rich_dens_2023
## `geom_smooth()` using formula = 'y ~ x'

x3 <- glm(Average_Evenness ~ shrub_density * aridity, data = final_data_2023)
x3
## 
## Call:  glm(formula = Average_Evenness ~ shrub_density * aridity, data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density                aridity  
##             0.1816823              0.0084948             -0.0469045  
## shrub_density:aridity  
##            -0.0009284  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  18 Residual
## Null Deviance:       0.1608 
## Residual Deviance: 0.009233  AIC: -98.64
anova(x3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     21   0.160797              
## shrub_density          1 0.013715        20   0.147082  2.33e-07 ***
## aridity                1 0.136519        19   0.010562 < 2.2e-16 ***
## shrub_density:aridity  1 0.001329        18   0.009233    0.1074    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Linear Model AIC:", AIC(x3), "\n")
## Linear Model AIC: -98.63904
quadratic_model_x3 <- glm(Average_Evenness ~ shrub_density + I(shrub_density^2) + aridity + I(aridity^2) + shrub_density:aridity, data = final_data_2023)
quadratic_model_x3
## 
## Call:  glm(formula = Average_Evenness ~ shrub_density + I(shrub_density^2) + 
##     aridity + I(aridity^2) + shrub_density:aridity, data = final_data_2023)
## 
## Coefficients:
##           (Intercept)          shrub_density     I(shrub_density^2)  
##             0.1963905              0.0105327             -0.0001974  
##               aridity           I(aridity^2)  shrub_density:aridity  
##            -0.0877876              0.0103750             -0.0008426  
## 
## Degrees of Freedom: 21 Total (i.e. Null);  16 Residual
## Null Deviance:       0.1608 
## Residual Deviance: 0.008405  AIC: -96.71
anova(quadratic_model_x3, test = "Chisq")
## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Average_Evenness
## 
## Terms added sequentially (first to last)
## 
## 
##                       Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                                     21   0.160797              
## shrub_density          1 0.013715        20   0.147082 3.226e-07 ***
## I(shrub_density^2)     1 0.020159        19   0.126922 5.833e-10 ***
## aridity                1 0.116561        18   0.010361 < 2.2e-16 ***
## I(aridity^2)           1 0.001096        17   0.009265    0.1485    
## shrub_density:aridity  1 0.000860        16   0.008405    0.2006    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cat("Quadratic Model AIC:", AIC(quadratic_model_x3), "\n")
## Quadratic Model AIC: -96.7066
if (AIC(quadratic_model_x1) < AIC(x1)) {
  cat("Quadratic model is better.\n")
} else {
  cat("Linear model is better or equally good.\n")
}
## Linear model is better or equally good.
even_dens_2023 <- ggplot(final_data_2023, aes(shrub_density, Average_Evenness)) +
geom_smooth(method = "lm", se = TRUE, color = "black") +
scale_color_brewer(palette = "Set1") +  labs(x = "Shrub Density per 20m Radius", y = "Evenness") + theme_classic() + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10))+
   labs(tag = "C") + theme(text = element_text(size = 12), panel.border = element_rect(color = "black", fill = NA, size = 1.5), axis.text = element_text(size = 10)) + theme(aspect.ratio = 0.7) + theme(legend.position = "none") + theme(legend.text = element_text(size = 8))
even_dens_2023
## `geom_smooth()` using formula = 'y ~ x'

plot2 <- abund_dens_2023/rich_dens_2023/even_dens_2023
plot2
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'